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On Irresolute topological vector spaces

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Advances in Pure Mathematics 2016年第2期6卷 105-112页

作者： Moizud Din Khan Muhammad Asad Iqbal Department of Mathematics COMSATS Institute of Information Technology Islamabad Pakistan

In this paper, our focus is to investigate the notion of irresolute topological vector spaces. Irresolute topological vector spaces are defined by using semi open sets and irresolute mappings. The notion of irresolute topological vector spaces is analog to the notion of topological vector spaces, but mathematically it behaves differently. An example is given to show that an irresolute topological vector space is not a topological vector space. It is proved that: 1) Irresolute topological vector spaces possess open hereditary property;2) A homomorphism of irresolute topological vector spaces is irresolute if and only if it is irresolute at identity element;3) In irresolute topological vector spaces, the scalar multiple of semi compact set is semi compact;4) In irresolute topological vector spaces, every semi open set is translationally invariant.

关键词： topological vector space Irresolute topological vector space Irresolue Mapping Semi Open Set

EXISTENCE OF SOLUTIONS FOR GENERALIZEDQUASI-VARIATIONAL-LIKE INEQUALITIES

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Applied Mathematics and Mechanics(English Edition) 1997年第2期18卷 141-150页

作者：丁协平 Department of Mathematics Sichuan Normal University Chengdu P. R. China

In this paper, some existence theorems of solutions for a class of generalized quasi-variational-like inequalities with discontinuous mappings ape proved under paracompact setting in topological vector spaces. These t... 详细信息

关键词： topological vector space generalized quasi-variational-like inequality 0-diagonally concave 0-diagonally concave relation

On Generalized vector Equilibrium Problems

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Acta Mathematicae Applicatae Sinica 2006年第1期22卷 21-26页

作者： An-hua Wan Jun-yi Fu Wei-hua Mao Department of Applied Mathematics South China Agricultural University Guangzhou 510642 China Department of Mathematics Nanchang University NaIlchang 330047 China

A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of... 详细信息

关键词： vector equilibrium problem set-valued mapping topological vector space KKM theorem

A Version of Ekeland's Variational Principle in Countable Semi-Normed spaces

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Journal of Mathematical Research and Exposition 2004年第1期24卷 1-6页

作者：丘京辉苏州大学数学系江苏苏州215006

In this paper, a now version of Ekeland's variational principle in countable semi-normed spaces is given.

关键词： Ekeland's variational principle topological vector space countable seminormed space.

QUASI-VARIATIONAL INEQUALITIES AND SOCIAL EQUILIBRIUM

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Applied Mathematics and Mechanics(English Edition) 1991年第7期12卷 639-646页

作者：丁协平 Sichuan Normal University Chengdu

A quasi-variational inequality is proved in paracompact setting which generalizes the results of Zhou Chen andAubin. As applications, two existence theorems on the solutions of optimization problems and social equilib... 详细信息

关键词： topological vector space minimax inequality generalized quasi-variational inequality optimization problem social equilibria

COVERING PROPERTIES ON H-spaceS AND APPLICATIONS

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Applied Mathematics and Mechanics(English Edition) 1993年第12期14卷 1079-1088页

作者：丁协平陈国强 Department of Mathematics Sichuan Normal University Chengdu Department of Mathematics Statistics and Computing Science Dalhousie University Halifax Nova Scotia Canada B3H 3J5

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.

关键词： covering property H-space H-convex H-convex hull almost fixed point lower semi-continuous l.c.-space simplex uniform structure topological vector space locally convex space,contractible

MAXIMAL ELEMENTS OF CONDENSING PREFERENCE MAPS IN LOCALLY CONVEX HAUSDORFF spaceS

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Applied Mathematics and Mechanics(English Edition) 1991年第8期12卷 741-744页

作者：丁协平 Department of Mathematics Sichuan Normal University Chengdu

Two existence theorems of maximal elements of condensing preference maps in locally convex Hausdorff spaces are proved which generalize the recent results of Mehta. One of them positively answers the open problem ment... 详细信息

关键词： topological vector space condensing preference map,maximal element

A Fixed Point Theorem and Some Generalized Ky Fan's Minimax Inequalities

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Communications in Mathematical Research 2011年第3期27卷 268-278页

作者： LUO XIAN-QIANG Science College Shanghai University Shanghai 200444 Mathematical College Wuyi University Jiangmen Guangdong 529020

In this paper, we establish a fixed point theorem for set-valued mapping on a topological vector space without ＂local convexity＂. And we also establish some generalized Ky Fan＇s minimax inequalities for set-value v... 详细信息

关键词： fixed point Ky Fan's minimax inequality set-valued vector mapping topological vector space

APPLICATIONS OF FIXED POINT THEOREMS TO INVARIANT APPROXIMATION

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Analysis in Theory and Applications 2000年第3期16卷 48-55页

作者： A.R.Khan N.Hussain A.B.Thaheem Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya UniversityMultan 60800Pakistan Department of Mathematical Science King Fahd University of Petroleum and MineralsDhahran 31261Saudi Arabia

We prove some fixed point theorems. As applications we obtain Brosowski-Meinardus type theorems on invariant approximations on a class of nonconvex sets in locally bounded topological vector spaces.

关键词： Compact Subset topological vector space Convex space Invariant Subset Strong Topology