In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the ...In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit bM1 in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spiraJlike mappings in several complex variables.展开更多
In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spa...In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.展开更多
Liczberski-Starkov firstfound a lower bound for ｜｜D（f）｜｜ near the origin, where f（z）=（F（z1）,√F1（z1）z2,…,√F＇（z1）zn）＇is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized c...Liczberski-Starkov firstfound a lower bound for ｜｜D（f）｜｜ near the origin, where f（z）=（F（z1）,√F1（z1）z2,…,√F＇（z1）zn）＇is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ｜｜D（f）｜｜ is obtained again.展开更多
In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt dom...In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.展开更多
In this paper, we get the fact that generalized Roper-Suffridge operators act on spirallike mapping of type α on different domains is invariable, these results include some results known.
This note induces some generalized Roper-Suffridge extension operators such that they are used to construct some almost starlike mappings of order α and starlike mappings of order a on different domains.
In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conc...In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ （β, A, B）, almost starlike mapping of complex order A on Ωn,p2……pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order a, strongly pirallikeness of type β and order a, almost starlikeness of order a on Ωn,p2……pn The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.展开更多
In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locall...In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.展开更多
Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…...Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…× Cnk： ｜z1｜^2＋ ｜｜z2｜｜2^p2＋ … ＋ ｜｜zk ｜｜k^pk〈 1} given〈1} give by F（z）=（f（z1）＋f＇（z1）∑j=2 kPj（zj,（f＇（z1））1/p2 z2＇,…,（f＇（z1））1/pkzk＇）＇, where f is a normaljized biholomorphic function k（z） =（f（z1） ＋ f′（z1）=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj ： C^nj→ C is a homogeneous polynomial of degree pj and zj =（zj1, …, zjnj）′∈ C^nj, nj ≥ 1, pj ≥ 1,｜｜zj｜｜j =（∑l=1 nj｜zjl｜^pj）1/pj. In this paper, some conditions for Pjare found under which the loperator p ｜zjl｜pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval...In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.展开更多
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective to...Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.展开更多
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference...Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.展开更多
In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,...In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.展开更多
Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I...Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I∈Z^(d))ξ(i)(ω)W(x-i)is a random potential term generated by a sequence of independent and identically distributed random variables{ξ(i)}_(i)∈Z^(d)and a non-negative measurable function W(x).In particular,the exact order of asymptotic properties of N(λ)depends on the decay properties of the reference function W(x)and the spectrum properties of the first Dirichlet eigenvalue of(-△)^(α/2).展开更多
In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovsk...In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.展开更多
基金supported by NSF of China(11271359)Science and Technology Research Projects of Henan Provincial Education Department(17A110041)Youth Fund Projects of Zhoukou Normal University(zknu B3201608)
文摘In this paper, we extend the Roper-Suffridge extension operator in complex Ba- nach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit bM1 in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spiraJlike mappings in several complex variables.
文摘In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.
基金Foundation item： Supported by the National Natural Science Foundation of China（10826083） Supported by the Zhejiang Provincial Natural Science Foundation of ChinaCD7080080）
文摘Liczberski-Starkov firstfound a lower bound for ｜｜D（f）｜｜ near the origin, where f（z）=（F（z1）,√F1（z1）z2,…,√F＇（z1）zn）＇is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ｜｜D（f）｜｜ is obtained again.
基金supported by the National Natural Science Foundation of China(11001246,11101139)Zhejiang Innovation Project(T200905)
文摘In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.
基金the National Natural Science Foundation of China(10571044)
文摘In this paper, we get the fact that generalized Roper-Suffridge operators act on spirallike mapping of type α on different domains is invariable, these results include some results known.
基金Project supported by NNSF of China (10571164,10626015,10571044)SRFDP of Higher Education (20050358052)the Natural Science Foundation of Henan University (04ZDZR004).
文摘This note induces some generalized Roper-Suffridge extension operators such that they are used to construct some almost starlike mappings of order α and starlike mappings of order a on different domains.
基金supported by NSFC(11271359,U1204618)Science and Technology Research Projects of Henan Provincial Education Department(14B110015,14B110016)Youth Fund Projects of Zhoukou Normal University(zknuB 3201608)
文摘In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of SΩ （β, A, B）, almost starlike mapping of complex order A on Ωn,p2……pn. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order a, strongly pirallikeness of type β and order a, almost starlikeness of order a on Ωn,p2……pn The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.
文摘In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.
基金Supported by the National Natural Science Foundation of China(11001074,11061015,11101124)
文摘Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…× Cnk： ｜z1｜^2＋ ｜｜z2｜｜2^p2＋ … ＋ ｜｜zk ｜｜k^pk〈 1} given〈1} give by F（z）=（f（z1）＋f＇（z1）∑j=2 kPj（zj,（f＇（z1））1/p2 z2＇,…,（f＇（z1））1/pkzk＇）＇, where f is a normaljized biholomorphic function k（z） =（f（z1） ＋ f′（z1）=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj ： C^nj→ C is a homogeneous polynomial of degree pj and zj =（zj1, …, zjnj）′∈ C^nj, nj ≥ 1, pj ≥ 1,｜｜zj｜｜j =（∑l=1 nj｜zjl｜^pj）1/pj. In this paper, some conditions for Pjare found under which the loperator p ｜zjl｜pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
基金Supported by NSFC (No.12361027)NSF of Inner Mongolia (No.2018MS01021)+1 种基金NSF of Shandong Province (No.ZR2020QA009)Science and Technology Innovation Program for Higher Education Institutions of Shanxi Province (No.2024L533)。
文摘In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
文摘Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.
文摘This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
基金supported by National Science Foundations of China(Grant No.11771340,12171373).
文摘Recently,Choe-Koo-Wang(J Funct Anal,2020,278)demonstrated the rigid phenomenon:The compact linear combination of composition operators under the Coefficient Non-cancellation Condition(CNC),implies that each difference is compact on the weighted Bergman space in the unit disk.Motivated by the subtle connection of composition operator theory on the weighted Bergman spaces,Korenblum spaces and bounded holomorphic function spaces,we first explore the rigid phenomenon which also holds on the Korenblum space over the unit ball.Furthermore,we discuss which difference of composition operators is compact when the compact combination of composition operators does not satisfy the condition(CNC)on Korenblum spaces and bounded holomorphic function spaces over the unit ball setting.
基金Supported by by Natural Science Foundation of Henan(202300410184 and242300421387)。
文摘In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.
基金supported by the National Natural Science Foundation of China(12071076)the Scientific Research Start-up Foundation of Fujian University of Technology(GY-Z23238)the Program for Education and Scientific Research of Young and Middle-Aged Teachers in Fujian Province(JAT191128,JT180818)。
文摘Explicit asymptotic properties of the integrated density of states N(λ)with respect to the spectrum for the random Schrödinger operator H^(ω)=(-△)^(α/2)+V^(ω)are established,whereα∈(0,2]and V^(ω)(X)=∑_(I∈Z^(d))ξ(i)(ω)W(x-i)is a random potential term generated by a sequence of independent and identically distributed random variables{ξ(i)}_(i)∈Z^(d)and a non-negative measurable function W(x).In particular,the exact order of asymptotic properties of N(λ)depends on the decay properties of the reference function W(x)and the spectrum properties of the first Dirichlet eigenvalue of(-△)^(α/2).
基金Supported by Fujian Provincial Natural Science Foundation of China(2024J01792)。
文摘In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.
