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Abstract and Applied Analysis
Volume 2013, Article ID 613928, 13 pages
http://dx.doi.org/10.1155/2013/613928
Research Article

A Unified Iterative Treatment for Solutions of Problems of Split Feasibility and Equilibrium in Hilbert Spaces

1Department of Accounting Information, Southern Taiwan University of Science and Technology, 1 Nantai Street, Yongkang District, Tainan 71005, Taiwan
2Department of Industrial Management, National Pingtung University of Science and Technology, 1 Shuefu Road, Neipu, Pingtung 91201, Taiwan

Received 21 May 2013; Revised 30 August 2013; Accepted 1 September 2013

Academic Editor: Simeon Reich

Copyright © 2013 Young-Ye Huang and Chung-Chien Hong. 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 at first raise the so called split feasibility fixed point problem which covers the problems of split feasibility, convex feasibility, and equilibrium as special cases and then give two types of algorithms for finding solutions of this problem and establish the corresponding strong convergence theorems for the sequences generated by our algorithms. As a consequence, we apply them to study the split feasibility problem, the zero point problem of maximal monotone operators, and the equilibrium problem and to show that the unique minimum norm solutions of these problems can be obtained through our algorithms. Since the variational inequalities, convex differentiable optimization, and Nash equilibria in noncooperative games can be formulated as equilibrium problems, each type of our algorithms can be considered as a generalized methodology for solving the aforementioned problems.