In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point res...In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.展开更多
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit...A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.展开更多
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U...Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.展开更多
In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,u...In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et ...A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.展开更多
A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in...A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.展开更多
We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and sev...We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.展开更多
A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operato...A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H（·, ·）-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.展开更多
In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of to...In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.展开更多
The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to t...The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.展开更多
A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely...A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.展开更多
The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets...The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.展开更多
The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh...The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.展开更多
Motivated by the result of Chen-Liu-Ru[1],we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(n) with ramification,which can be seen as a...Motivated by the result of Chen-Liu-Ru[1],we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(n) with ramification,which can be seen as a generalization of the results in the case of the minimal surfaces.In addition,we give an estimate of the Gauss curvature for the K-quasiconfomal harmonic surfaces whose generalized Gauss map is ramified over a set of hyperplanes.展开更多
By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy imp...The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.展开更多
基金funded by National Science,Research and Innovation Fund(NSRF)King Mongkut's University of Technology North Bangkok with Contract No.KMUTNB-FF-68-B-46.
文摘In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.
文摘A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map.
文摘Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province（2004110008）
文摘In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
基金The foundation project of Chengdu University of Information Technology (No.CRF200502)
文摘A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.
文摘A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.
基金supported by Grant No.174025 of the Ministry of Science,Technology and Development,Republic of Serbiasupported by Universita` degli Studi di Palermo,Local project R.S.ex 60%
文摘We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.
基金Supported by the National Natural Science Foundation of China(Grant No.11371015)the Key Project of Chinese Ministry of Education(Grant No.211163)+3 种基金Sichuan Youth Science and Technology Foundation(GrantNo.2012JQ0032)the Foundation of China West Normal University(Grant No.11A028,11A029)the Fundamental Research Funds of China West Normal University(Grant No.13D016)the Natural Science Foundation ofSichuan Provincial Education Department(Grant No.14ZB0142)
文摘A new system of set-valued variational inclusions involving generalized H（·, ·）-accretive mapping in real q-uniformly smooth Banach spaces is introduced, and then based on the generalized resolvent operator technique associated with H（·, ·）-accretivity, the existence and approximation solvability of solutions using an iterative algorithm is investigated.
文摘In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.
基金supported by the National Natural Science Foundation of China(61373174)
文摘The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.
文摘A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.
文摘The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function ?which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function;that is, for all measurable sets.?Such a property is not shared by vector valued set functions. We introduce a suitable definition of the integral that will extend the above property to the vector valued case in its full generality. We also discuss a further extension of the Fundamental Theorem of Calculus for additive set functions with values in an infinite dimensional normed space.
基金the National Natural Science Foundation(69972036) and the Natural Science Foundation of Shanxi province(995L02)
文摘The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.
基金supported by the Fundamental Research Funds for the Central Universities(500421360)supported by NNSF of China(11571049,12071047)+1 种基金supported by NNSF of China(11971182)NSF of Fujian Province of China(2019J01066)。
文摘Motivated by the result of Chen-Liu-Ru[1],we investigate the value distribution properties for the generalized Gauss maps of weakly complete harmonic surfaces immersed in R^(n) with ramification,which can be seen as a generalization of the results in the case of the minimal surfaces.In addition,we give an estimate of the Gauss curvature for the K-quasiconfomal harmonic surfaces whose generalized Gauss map is ramified over a set of hyperplanes.
基金Supported by the National Natural Science Foundation of China (10571035)
文摘By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.
基金supported by the National Natural Science Foundation of China(60774100)the Natural Science Foundation of Shandong Province of China(Y2007A15)
文摘The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.
