In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence t...In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].展开更多
Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbau...Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.展开更多
In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.展开更多
Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two ...Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.展开更多
In Refs. [1] and [2], the authors gave the solutions of linear systems of a class with ranges in a Banach space. In distributed parameter systems, because many spaces of the functions of solutions are not Banach space...In Refs. [1] and [2], the authors gave the solutions of linear systems of a class with ranges in a Banach space. In distributed parameter systems, because many spaces of the functions of solutions are not Banach spaces, we need extend the scope of the space to a locally convex space. Suppose that E is a complete separated locally convex space, E’ is the dual space of E, R^+ is a set of non-negative numbers, C is a set of all complex numbers, and P,展开更多
文摘In this paper we investigate generalized bi quasi variational inequalities in locally convex topological vector spaces. Motivated and inspired by the recent research work in this field,we establish several existence theorems of solutions for generalized bi quasi variational inequalities,which are the extension and improvements of the earlier and recent results obtained previously by many authors including Sun and Ding [18],Chang and Zhang [23] and Zhang [24].
基金This project partially supported by National Natural Science Foundation of ChinaThis work was partially supported by NSERC of Canada under grant A-8096
文摘Several theorems on closed (resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.
基金the National Natural Science Foundation of China (60274016)the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
文摘In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.
基金Supported by National Natural Science Foundation of China(Grant No.10871016)
文摘Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.
文摘In Refs. [1] and [2], the authors gave the solutions of linear systems of a class with ranges in a Banach space. In distributed parameter systems, because many spaces of the functions of solutions are not Banach spaces, we need extend the scope of the space to a locally convex space. Suppose that E is a complete separated locally convex space, E’ is the dual space of E, R^+ is a set of non-negative numbers, C is a set of all complex numbers, and P,
