In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known clas...In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered.展开更多
Let S_s*be the class of normalized functions f defined in the open unit■such that the quantity zf’(z)/f(z)lies in an eight-shaped region in the right-half plane and satisfies the condition■.In this paper,we aim to ...Let S_s*be the class of normalized functions f defined in the open unit■such that the quantity zf’(z)/f(z)lies in an eight-shaped region in the right-half plane and satisfies the condition■.In this paper,we aim to investigate Toeplitz determinants for the inverse of this function classes S_s*associated with sine function.展开更多
Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f i...Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.展开更多
In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are...In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.展开更多
In this paper, we consider a new class CS＊s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function φ（z, s, a）. Basi...In this paper, we consider a new class CS＊s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function φ（z, s, a）. Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.展开更多
For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Feket...For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.展开更多
In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established,Integral transforms of functions in these classes are also considered.In parti...In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established,Integral transforms of functions in these classes are also considered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe[4]and Bajpai[5].展开更多
M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the...M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.展开更多
Let S(p)be the class of all univalent meromorphic functions f on the unit disk D with a simple pole at p∈(0,1).Forα∈[0,1),we denote byΣ^(*)(p,ω_(0),α)the class of f∈E S(p)such that C\f(D)is a starlike domain of...Let S(p)be the class of all univalent meromorphic functions f on the unit disk D with a simple pole at p∈(0,1).Forα∈[0,1),we denote byΣ^(*)(p,ω_(0),α)the class of f∈E S(p)such that C\f(D)is a starlike domain of orderαwith respect to fixed pointω_(0)≠0,∞.In this paper,some analytic characterizations and coefficient estimates of f∈∑^(*)(p,ω_(0),α)are considered.展开更多
In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions bel...In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.展开更多
Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1...Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.展开更多
In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coef...In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.展开更多
This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（...This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.展开更多
We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,an...We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.展开更多
The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operatorsεα,λ^γand Hm^l(α1)related to the generalized Mittag-Leffler function Eα,λ^γand the g...The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operatorsεα,λ^γand Hm^l(α1)related to the generalized Mittag-Leffler function Eα,λ^γand the generalized hypergeometric function,defined in the unit disk,respectively.The results presented here make connections to some of the earlier known developments.展开更多
This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety, where α_ is unique solution of equation (αα)^(1/2)=σwith a in (0.1),and α-[1+(1-2α)r^(2n)]/(1-r^(2n)),σ =[1-(1-2α)r~]...This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety, where α_ is unique solution of equation (αα)^(1/2)=σwith a in (0.1),and α-[1+(1-2α)r^(2n)]/(1-r^(2n)),σ =[1-(1-2α)r~]/(1+r~).Futhermore,we consider an extension of class S(α,n):Let S(α、β、n) denote the class of functions f(z)=z+α_z^(n+1)+…(n≥1)that are analytie in |z|<1 such that f(z)/g (z)∈p(α,n)[1],where g(z)∈S~*(β)[2].This paper prove that the radius of starlikeness of class S(α, β,n) is given by the smallest positive root(less than 1)of the following equations (1-2α)(1-2β)r^(2)-2[1-α-β-n(1-α)]r^+1=0.0≤α≤α_0, (1-α)[1-(1-2β)r~]-n[r^(1+r^)=0.,α_0≤α<1. where α=[1+(1-2α)r^(2)]/(1-r^(2)(0≤r<1),α_0(?(0,1) is some fixed number.This result is also the cxtension of well-known results[T.Th3] and [8,Th3]展开更多
In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a corr...In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.展开更多
By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1...By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1 + α{1 +z[_lI_mf(z)]′′/[_lI_mf(z)]′}/z[_lI_mf(z)]′/_lI_mf(z))■φ(z)(α ∈ C-{1/2, 1}).展开更多
文摘In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered.
基金Supported by the National Natural Science Foundation of China(Grant No.11561001)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-18-A14)+4 种基金the Natural Science Foundation of Inner Mongolia of China(Grant No.2018MS01026)the Higher School Foundation of Inner Mongolia of China(Grant No.NJZY19211)the Natural Science Foundation of Anhui Provincial Department of Education(Grant No.KJ2018A0833)Provincial Quality Engineering Project of Anhui Colleges and Universities(Grant No.2018mooc608)the Key Cultivated Project at School Level of the National Science Fund of Guangzhou Civil Aviation College(Grant Nos.18X0428,18X0433)。
文摘Let S_s*be the class of normalized functions f defined in the open unit■such that the quantity zf’(z)/f(z)lies in an eight-shaped region in the right-half plane and satisfies the condition■.In this paper,we aim to investigate Toeplitz determinants for the inverse of this function classes S_s*associated with sine function.
基金supported by the Grant No.20-16367/NRPU/RD/HEC/20212021。
文摘Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
基金Supported by the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2020A 0993KJ2020ZD74)+2 种基金the High-Level Talent Research Start-Up Project(Grant No.DC2300000286)the Foundation of Guangzhou Civil Aviation College(Grant Nos.22X041824X4412).
文摘In the paper,a class of functions with bounded turnings involving cardioid domain,are studied in the region of the unit disc.The bounds of|a_(5)|,|a_(6)|,|a_(7)|and the fourth Hankel determinant are obtained,which are more accurate than those obtained by Srivastava.
文摘In this paper, we consider a new class CS＊s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function φ（z, s, a）. Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.
文摘For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.
文摘In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
文摘In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established,Integral transforms of functions in these classes are also considered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe[4]and Bajpai[5].
基金This research was supported by NNSF of China(Grant No.10231040)NCET(06-0504)
文摘M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.
基金Supported by the National Natural Science Foundation of China(Grant No.11871215)。
文摘Let S(p)be the class of all univalent meromorphic functions f on the unit disk D with a simple pole at p∈(0,1).Forα∈[0,1),we denote byΣ^(*)(p,ω_(0),α)the class of f∈E S(p)such that C\f(D)is a starlike domain of orderαwith respect to fixed pointω_(0)≠0,∞.In this paper,some analytic characterizations and coefficient estimates of f∈∑^(*)(p,ω_(0),α)are considered.
基金Supported by the National Natural Science Foundation of China(Grant No.11271045)the Funds of Doctoral Programme of China(Grant No.20100003110004)the Natural Science Foundation of Inner Mongolia Province(Grant No.2010MS0117)
文摘In this paper, we introduce new subclasses Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）of certain p-valent analytic functions defined by a generalized differential operator. Majorizationproperties for functions belonging to the classes Sp,q,^mj,l λ[A,B;γ]and Hp,q,λ^m,j,l（α,β）are investigated. Also, we point out some new or known consequences of our main results.
基金Supported by the Key Laboratory of Applied Mathematics in Hubei Province,China
文摘Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.
文摘In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.
文摘This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.
文摘We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.
基金the Youth Science Fund Research Project of Pingxiang University(Grant Nos.2019D0202,2018D0218,2018D0208)the Youth Fund Project of Science and Technology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ191157)。
文摘The aim of the present paper is to investigate some sufficient conditions for starlikeness and convexity of two new operatorsεα,λ^γand Hm^l(α1)related to the generalized Mittag-Leffler function Eα,λ^γand the generalized hypergeometric function,defined in the unit disk,respectively.The results presented here make connections to some of the earlier known developments.
文摘This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety, where α_ is unique solution of equation (αα)^(1/2)=σwith a in (0.1),and α-[1+(1-2α)r^(2n)]/(1-r^(2n)),σ =[1-(1-2α)r~]/(1+r~).Futhermore,we consider an extension of class S(α,n):Let S(α、β、n) denote the class of functions f(z)=z+α_z^(n+1)+…(n≥1)that are analytie in |z|<1 such that f(z)/g (z)∈p(α,n)[1],where g(z)∈S~*(β)[2].This paper prove that the radius of starlikeness of class S(α, β,n) is given by the smallest positive root(less than 1)of the following equations (1-2α)(1-2β)r^(2)-2[1-α-β-n(1-α)]r^+1=0.0≤α≤α_0, (1-α)[1-(1-2β)r~]-n[r^(1+r^)=0.,α_0≤α<1. where α=[1+(1-2α)r^(2)]/(1-r^(2)(0≤r<1),α_0(?(0,1) is some fixed number.This result is also the cxtension of well-known results[T.Th3] and [8,Th3]
文摘In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.
基金The NSF(KJ2015A372)of Anhui Provincial Department of Education
文摘By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1 + α{1 +z[_lI_mf(z)]′′/[_lI_mf(z)]′}/z[_lI_mf(z)]′/_lI_mf(z))■φ(z)(α ∈ C-{1/2, 1}).
