Open Access

Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

Journal of Inequalities and Applications20082007:020457

https://doi.org/10.1155/2007/20457

Received: 31 July 2007

Accepted: 3 December 2007

Published: 23 January 2008

Abstract

We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert spaces. We also study the convergence criteria of iterative methods under some mild conditions. Our results improve and extend the recent ones announced by many others.

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Authors’ Affiliations

(1)
Department of Mathematics and the RINS, Gyeongsang National University
(2)
Department of Mathematics, Shijiazhuang University

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Copyright

© X. Qin and M. Shang 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.