Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 290713, 13 pages
doi:10.1155/2009/290713
Research Article

Perturbed Iterative Approximation of Solutions for Nonlinear General A-Monotone Operator Equations in Banach Spaces

Xing Wei,1 Heng-you Lan,2 and Xian-jun Zhang2

1College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China
2Department of Mathematics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, China

Received 2 January 2009; Accepted 19 March 2009

Academic Editor: Ram U. Verma

Copyright © 2009 Xing Wei 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

We introduce and study a new class of nonlinear general A-monotone operator equations with multivalued operator. By using Alber's inequalities, Nalder's results, and the new proximal mapping technique, we construct some new perturbed iterative algorithms with mixed errors for solving the nonlinear general A-monotone operator equations and study the approximation-solvability of the nonlinear operator equations in Banach spaces. The results presented in this paper improve and generalize the corresponding results on strongly monotone quasivariational inclusions and nonlinear implicit quasivariational inclusions.