Open Access

Perturbed Iterative Algorithms for Generalized Nonlinear Set-Valued Quasivariational Inclusions Involving Generalized -Accretive Mappings

Journal of Inequalities and Applications20072007:029863

DOI: 10.1155/2007/29863

Received: 24 August 2006

Accepted: 14 January 2007

Published: 22 March 2007

Abstract

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalized -accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized -accretive mappings, we established the equivalence between the generalized nonlinear set-valued quasi-variational inclusions and the fixed point problems, and some new perturbed iterative algorithms, proved that its proximate solution converges strongly to its exact solution in real Banach spaces.

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Authors’ Affiliations

(1)
Department of Mathematics, Yangtze Normal University

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Copyright

© Mao-Ming Jin 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.