Journal of Applied Mathematics
Volume 2012 (2012), Article ID 720192, 14 pages
http://dx.doi.org/10.1155/2012/720192
Research Article

Implicit and Explicit Iterations with Meir-Keeler-Type Contraction for a Finite Family of Nonexpansive Semigroups in Banach Spaces

Jiancai Huang,1 Shenghua Wang,2 and Yeol Je Cho3

1School of Control and Computer Engineering, North China Electric Power University, Baoding 071003, China
2School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
3Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

Received 31 December 2011; Accepted 28 January 2012

Academic Editor: Rudong Chen

Copyright © 2012 Jiancai Huang et al. 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 an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir-Keeler-type contraction in a Banach space. Then we prove the strong convergence for the implicit and explicit iterative schemes. Our results extend and improve some recent ones in literatures.