Open Access

A New System of Nonlinear Fuzzy Variational Inclusions Involving -Accretive Mappings in Uniformly Smooth Banach Spaces

Journal of Inequalities and Applications20092009:806727

DOI: 10.1155/2009/806727

Received: 4 October 2009

Accepted: 4 November 2009

Published: 23 November 2009

Abstract

A new system of nonlinear fuzzy variational inclusions involving -accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion) problems as special cases of this system. By using the resolvent operator technique associated with -accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran
(2)
Department of Mathematics, King's College London Strand
(3)
Department of Mathematics Education and the RINS, Gyeongsang National University

Copyright

© M. Alimohammady et al. 2009

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.