On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxedη−αMonotone Mapping-Reference-Cited by-同舟云学术

On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxedη−αMonotone Mapping

Published:2013 Issue: Volume:2013 Page:1-8
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Kutbi Marwan Amin¹,Sintunavarat Wutiphol²^ORCID

Affiliation:

1. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

2. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12121, Thailand

Abstract

We introduce two new concepts of weakly relaxedη-αmonotone mappings and weakly relaxedη-αsemimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxedη-αmonotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxedη-αsemimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.

Funder

King Abdulaziz University

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2013/207845.pdf

Reference23 articles.

1. On the generalized monotonicity of variational inequalities

2. Variational inequalities for monotone operators in nonreflexive Banach spaces

3. Some relations between variational-like inequality problems and vectorial optimization problems in Banach spaces