Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 840978, 12 pages
doi:10.1155/2011/840978
Research Article

The Over-Relaxed 𝐴 -Proximal Point Algorithm for General Nonlinear Mixed Set-Valued Inclusion Framework

Xian Bing Pan,1 Hong Gang Li,2 and An Jian Xu3

1Yitong College, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Institute of Applied Mathematics Research, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
3College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China

Received 16 November 2010; Accepted 10 January 2011

Academic Editor: T. Benavides

Copyright © 2011 Xian Bing Pan 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

The purpose of this paper is (1) a general nonlinear mixed set-valued inclusion framework for the over-relaxed 𝐴 -proximal point algorithm based on the ( 𝐴 , 𝜂 )-accretive mapping is introduced, and (2) it is applied to the approximation solvability of a general class of inclusions problems using the generalized resolvent operator technique due to Lan-Cho-Verma, and the convergence of iterative sequences generated by the algorithm is discussed in 𝑞 -uniformly smooth Banach spaces. The results presented in the paper improve and extend some known results in the literature.