Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 501293, 12 pages
doi:10.1155/2010/501293
Research Article

An Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem Based on (A,η)-Accretive Framework

Hong Gang Li,1 An Jian Xu,1 and Mao Ming Jin2

1Institute of Applied Mathematics Research, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Institute of Nonlinear Analysis Research, Changjiang Normal University, Fuling Chongqing, 400803, China

Received 30 April 2010; Accepted 8 June 2010

Academic Editor: Massimo Furi

Copyright © 2010 Hong Gang Li 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 general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of (A,η)-accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to (A,η)-accretive mapping due to Lan-Cho-Verma in Banach space. The result that sequence {xn} generated by the algorithm converges linearly to a solution of the nonlinear set-valued inclusions problem with the convergence rate θ is proved.