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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 153456, 16 pages
http://dx.doi.org/10.1155/2012/153456
Research Article

Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities

Department of Mathematics, Dong-A University, Busan 604-714, Republic of Korea

Received 1 December 2011; Accepted 9 January 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Jong Soo Jung. 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 new implicit and explicit algorithms for finding the fixed point of a k-strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a fixed point of a k-strictly pseudocontractive mapping. Such a point is also a solution of a variational inequality defined on the set of fixed points. As direct consequences, we obtain the unique minimum-norm fixed point of a k-strictly pseudocontractive mapping.