Abstract and Applied Analysis
Volume 2012 (2012), Article ID 789043, 12 pages
http://dx.doi.org/10.1155/2012/789043
Research Article

Fixed Point and Weak Convergence Theorems for ( 𝛼 , 𝛽 ) -Hybrid Mappings in Banach Spaces

Tian-Yuan Kuo,1 Jyh-Chung Jeng,2 Young-Ye Huang,3 and Chung-Chien Hong4

1Center for General Education, Fooyin University, 151 Jinxue Road, Daliao District, Kaohsiung 83102, Taiwan
2Department of Finance, Nan Jeon Institute of Technology, 178 Chaoqin Road, Yenshui District, Tainan 73746, Taiwan
3Center for General Education, Southern Taiwan University, 1 Nantai Street, Yongkang District, Tainan 71005, Taiwan
4Department of Industrial Management, National Pingtung University of Science and Technology, 1 Shuefu Road, Neopu, Pingtung 91201, Taiwan

Received 28 September 2011; Accepted 29 November 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Tian-Yuan Kuo 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 the class of ( 𝛼 , 𝛽 ) -hybrid mappings relative to a Bregman distance 𝐷 𝑓 in a Banach space, and then we study the fixed point and weak convergence problem for such mappings.