## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 430409, 8 pages.

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

Kamonrat Sombut and Somyot Plubtieng

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#### 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), Article ID 430409, 8 pages.

**Dates**

First available in Project Euclid: 18 April 2013

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1155/2013/430409

**Mathematical Reviews number (MathSciNet)**

MR3035187

**Zentralblatt MATH identifier**

1263.65063

#### Citation

Sombut, Kamonrat; Plubtieng, Somyot. Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems. Abstr. Appl. Anal. 2013 (2013), Article ID 430409, 8 pages. doi:10.1155/2013/430409. http://projecteuclid.org/euclid.aaa/1366306763.

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