A Maximal Element Theorem in FWC-Spaces and Its Applications

A Maximal Element Theorem in FWC-Spaces and Its Applications

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equil...

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Main Authors: Haishu Lu, Qingwen Hu, Yulin Miao
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:The Scientific World Journal
Online Access:http://dx.doi.org/10.1155/2014/890696
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spelling doaj-ae5013ab4c884910837b4ce7838cf7c52020-11-25T02:46:55ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/890696890696A Maximal Element Theorem in FWC-Spaces and Its ApplicationsHaishu Lu0Qingwen Hu1Yulin Miao2School of Business, Jiangsu University of Technology, Changzhou, Jiangsu 213001, ChinaDepartment of Mathematical Sciences, University of Texas at Dallas, Richardson, TX 75080, USASchool of Business, Jiangsu University of Technology, Changzhou, Jiangsu 213001, ChinaA maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature.http://dx.doi.org/10.1155/2014/890696
collection DOAJ
language English
format Article
sources DOAJ
author Haishu Lu
Qingwen Hu
Yulin Miao
spellingShingle Haishu Lu
Qingwen Hu
Yulin Miao
A Maximal Element Theorem in FWC-Spaces and Its Applications
The Scientific World Journal
author_facet Haishu Lu
Qingwen Hu
Yulin Miao
author_sort Haishu Lu
title A Maximal Element Theorem in FWC-Spaces and Its Applications
title_short A Maximal Element Theorem in FWC-Spaces and Its Applications
title_full A Maximal Element Theorem in FWC-Spaces and Its Applications
title_fullStr A Maximal Element Theorem in FWC-Spaces and Its Applications
title_full_unstemmed A Maximal Element Theorem in FWC-Spaces and Its Applications
title_sort maximal element theorem in fwc-spaces and its applications
publisher Hindawi Limited
series The Scientific World Journal
issn 2356-6140
1537-744X
publishDate 2014-01-01
description A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results represented in this paper unify and extend some known results in the literature.
url http://dx.doi.org/10.1155/2014/890696
work_keys_str_mv AT haishulu amaximalelementtheoreminfwcspacesanditsapplications
AT qingwenhu amaximalelementtheoreminfwcspacesanditsapplications
AT yulinmiao amaximalelementtheoreminfwcspacesanditsapplications
AT haishulu maximalelementtheoreminfwcspacesanditsapplications
AT qingwenhu maximalelementtheoreminfwcspacesanditsapplications
AT yulinmiao maximalelementtheoreminfwcspacesanditsapplications
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