Open Access Research

Convergence of algorithms for fixed points of generalized asymptotically quasi-ϕ-nonexpansive mappings with applications

Xiaolong Qin1, Ravi P Agarwal2, Sun Y Cho3* and Shin M Kang4*

Author Affiliations

1 Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

2 Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA

3 Department of Mathematics, Gyeongsang National University, Jinju 660-701, Republic of Korea

4 Department of Mathematics and RINS, Gyeongsang National University, Jinju 660-701, Republic of Korea

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Fixed Point Theory and Applications 2012, 2012:58 doi:10.1186/1687-1812-2012-58

Published: 13 April 2012

Abstract

In this article, strong convergence of Krasnoselski-Mann iterative sequences and Halpern iterative sequences are investigated based on hybrid projection methods. Strong convergence theorems for common fixed points of a family of generalized asymptotically quasi-ϕ-nonexpansive mappings are established in the framework of Banach spaces.

Mathematics Subject Classification 2000: 47H09; 47J05; 47J25

Keywords:
asymptotically quasi-ϕ-nonexpansive mapping; asymptotically nonexpansive mapping; fixed point; generalized asymptotically quasi-ϕ-nonexpansive mapping; generalized asymptotically quasi-nonexpansive mapping