Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 451916, 10 pages
doi:10.1155/2010/451916
Research Article

Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces

Jong Kyu Kim1 and Nguyen Buong2

1Department of Mathematics Education, Kyungnam University, Masan 631-701, South Korea
2Department of Mathematics, Vietnamse Academy of Science and Technology, Institute of Information Technology, 18, Hoang Quoc Viet, q. Cau Giay, Ha Noi 122100, Vietnam

Received 1 November 2009; Accepted 12 December 2009

Academic Editor: Yeol J. E. Cho

Copyright © 2010 Jong Kyu Kim and Nguyen Buong. 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 to present a regularization variant of the inertial proximal point algorithm for finding a common element of the set of solutions for a variational inequality problem involving a hemicontinuous monotone mapping A and for a finite family of λi-inverse strongly monotone mappings {Ai}i=1N from a closed convex subset K of a Hilbert space H into H.