Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 29863, 12 pages
doi:10.1155/2007/29863
Research Article

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

Mao-Ming Jin

 Department of Mathematics, Yangtze Normal University, Chongqing 408003, Fuling, China
Received 24 August 2006; Revised 10 January 2007; Accepted 14 January 2007

Recommended by H. Bevan Thompson

Abstract

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalized m-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 m-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.