## Abstract and Applied Analysis

### Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

#### Abstract

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.

#### Article information

Source
Abstr. Appl. Anal. Volume 2013 (2013), 8 pages.

Dates
First available in Project Euclid: 18 April 2013

http://projecteuclid.org/euclid.aaa/1366306763

Digital Object Identifier
doi:10.1155/2013/430409

Mathematical Reviews number (MathSciNet)
MR3035187

#### Citation

Sombut, Kamonrat; Plubtieng, Somyot. Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems. Abstract and Applied Analysis 2013 (2013), 1--8. doi:10.1155/2013/430409. http://projecteuclid.org/euclid.aaa/1366306763.

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