Open Access Research

Convergence theorems for mixed type asymptotically nonexpansive mappings

Weiping Guo1, Yeol Je Cho2* and Wei Guo3

Author Affiliations

1 School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, Jiangsu, 215009, P.R. China

2 Department of Mathematics Education and the RINS College of Education, Gyeongsang National University, Chinju, 660-701, Korea

3 Department of Aerospace Engineering and Mechanics, University of Minnesota, Twin Cities, Minneapolis, MN, 55455, USA

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Fixed Point Theory and Applications 2012, 2012:224  doi:10.1186/1687-1812-2012-224

Published: 11 December 2012

Abstract

In this paper, we introduce a new two-step iterative scheme of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong and weak convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.

Keywords:
mixed type asymptotically nonexpansive mapping; strong and weak convergence; common fixed point; uniformly convex Banach space