In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A ...In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.展开更多
A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff funct...A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.展开更多
Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed po...Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed points and Radon Nikodym-property is established.展开更多
The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
In this paper we study the dynamical behavior of a system ?approximated uniformly by a sequence ?of chaotic maps. We give examples to show that properties like sensitivity and denseness of periodic points need not be ...In this paper we study the dynamical behavior of a system ?approximated uniformly by a sequence ?of chaotic maps. We give examples to show that properties like sensitivity and denseness of periodic points need not be preserved under uniform convergence. We derive conditions under which some of the dynamical properties of the maps ?are preserved in .展开更多
For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array ...For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.展开更多
In this paper,we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract,and that it also admits the uniform compact approximation property.These can be regarded as extensio...In this paper,we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract,and that it also admits the uniform compact approximation property.These can be regarded as extensions of Lindenstrauss and Kalton's corresponding results.展开更多
The concepts of complex locally uniform rotundity and complex locally uniformly rotund point are introduced. The sufficient and necessary conditions of them are given in complex Musielak-Orlicz spaces.
基金supported by the National Natural Science Foundation of China(11671252)supported by the National Natural Science Foundation of China(11771278)
文摘In this article, we prove the following results： （1） A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; （2） A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.
基金the Natural Science Foundation of Education Department of Sichuan Province of China(No.07ZA092)the Foundation of Taiwan Science Council
文摘A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.
文摘Three characteristics of the very rotund space ape proved and the relationships between the very rotund space and the geometrical properties of Banach space are discussed. Also connection between the weakly exposed points and Radon Nikodym-property is established.
文摘The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
文摘In this paper we study the dynamical behavior of a system ?approximated uniformly by a sequence ?of chaotic maps. We give examples to show that properties like sensitivity and denseness of periodic points need not be preserved under uniform convergence. We derive conditions under which some of the dynamical properties of the maps ?are preserved in .
基金Supported by the National Natural Science F oundation of China(No.10071058)
文摘For weighted sums of the form?j=1kn anj Xnj\sum{_{j=1}^{k_(n)}}a_({nj})X_({nj})where{a_(nj),1?j?k_(n)↑∞,n?1}is a real constant array and{X_(aj),1≤j≤k n,n≥1}is a rowwise independent,zero mean,random element array in a real separable Banach space of typep,we establishL r convergence theorem and a general weak law of large numbers respectively,conversely,we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums.
基金Support by National Natural Science Foundation of China(Grant Nos.11731010,12071389)。
文摘In this paper,we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract,and that it also admits the uniform compact approximation property.These can be regarded as extensions of Lindenstrauss and Kalton's corresponding results.
基金This work was supported by the National Natural Science Foundation of China (Grant No.19871020)
文摘The concepts of complex locally uniform rotundity and complex locally uniformly rotund point are introduced. The sufficient and necessary conditions of them are given in complex Musielak-Orlicz spaces.
基金Supported by the National Natural Science Foundation of China(10661001)partially by the Guangxi Natural Science Foundation(0832275)the Natural Science Foundation of Liuzhou Teacher's College(LSZ2007A003)
