Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 806727, 33 pages
doi:10.1155/2009/806727
Research Article

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

M. Alimohammady,1,2 J. Balooee,1 Y. J. Cho,3 and M. Roohi1

1Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, Iran
2Department of Mathematics, King's College London Strand, London WC2R 2LS, UK
3Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea

Received 4 October 2009; Accepted 4 November 2009

Academic Editor: Charles E. Chidume

Copyright © 2009 M. Alimohammady et al. 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.

Abstract

A new system of nonlinear fuzzy variational inclusions involving (A,η)-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 (A,η)-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.