## Abstract and Applied Analysis

### Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi--Asymptotically Nonexpansive Mappings

#### Abstract

We introduce a modified block hybrid projection algorithm for solving the convex feasibility problems for an infinite family of closed and uniformly quasi-$\phi$-asymptotically nonexpansive mappings and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 357120, 22 pages.

Dates
First available in Project Euclid: 1 November 2010

https://projecteuclid.org/euclid.aaa/1288620743

Digital Object Identifier
doi:10.1155/2010/357120

Mathematical Reviews number (MathSciNet)
MR2669086

Zentralblatt MATH identifier
1206.47084

#### Citation

Saewan, Siwaporn; Kumam, Poom. Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi- -Asymptotically Nonexpansive Mappings. Abstr. Appl. Anal. 2010 (2010), Article ID 357120, 22 pages. doi:10.1155/2010/357120. https://projecteuclid.org/euclid.aaa/1288620743