Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems

Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems

By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium problem, and an existence theorem of system...

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Main Author: Wei-Shih Du
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2011/247236
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spelling doaj-0788c532043b42c7bbef3c8d313abd9d2020-11-24T23:54:51ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/247236247236Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization ProblemsWei-Shih Du0Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, TaiwanBy applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium problem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem is also given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed point theorem, and maximal element theorem.http://dx.doi.org/10.1155/2011/247236
collection DOAJ
language English
format Article
sources DOAJ
author Wei-Shih Du
spellingShingle Wei-Shih Du
Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
Abstract and Applied Analysis
author_facet Wei-Shih Du
author_sort Wei-Shih Du
title Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
title_short Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
title_full Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
title_fullStr Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
title_full_unstemmed Applications of an HIDS Theorem to the Existence of Fixed Point, Abstract Equilibria and Optimization Problems
title_sort applications of an hids theorem to the existence of fixed point, abstract equilibria and optimization problems
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2011-01-01
description By applying hybrid inclusion and disclusion systems (HIDS), we establish several vectorial variants of system of Ekeland's variational principle on topological vector spaces, some existence theorems of system of parametric vectorial quasi-equilibrium problem, and an existence theorem of system of the Stampacchia-type vectorial equilibrium problem. As an application, a vectorial minimization theorem is also given. Moreover, we discuss some equivalence relations between our vectorial variant of Ekeland's variational principle, common fixed point theorem, and maximal element theorem.
url http://dx.doi.org/10.1155/2011/247236
work_keys_str_mv AT weishihdu applicationsofanhidstheoremtotheexistenceoffixedpointabstractequilibriaandoptimizationproblems
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