On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping

On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping

We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain th...

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Main Authors: Marwan Amin Kutbi, Wutiphol Sintunavarat
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/207845
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spelling doaj-4b3fd563aad94a748152eae50869af1e2020-11-24T22:03:03ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/207845207845On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone MappingMarwan Amin Kutbi0Wutiphol Sintunavarat1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12121, ThailandWe introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.http://dx.doi.org/10.1155/2013/207845
collection DOAJ
language English
format Article
sources DOAJ
author Marwan Amin Kutbi
Wutiphol Sintunavarat
spellingShingle Marwan Amin Kutbi
Wutiphol Sintunavarat
On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
Abstract and Applied Analysis
author_facet Marwan Amin Kutbi
Wutiphol Sintunavarat
author_sort Marwan Amin Kutbi
title On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
title_short On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
title_full On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
title_fullStr On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
title_full_unstemmed On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
title_sort on the solution existence of variational-like inequalities problems for weakly relaxed η−α monotone mapping
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.
url http://dx.doi.org/10.1155/2013/207845
work_keys_str_mv AT marwanaminkutbi onthesolutionexistenceofvariationallikeinequalitiesproblemsforweaklyrelaxedēamonotonemapping
AT wutipholsintunavarat onthesolutionexistenceofvariationallikeinequalitiesproblemsforweaklyrelaxedēamonotonemapping
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