Convergence theorems for generalized nonexpansive mappings in uniformly convex Banach spaces

Fixexd point theory and applications

Mihai Postolache²  Balwant Singh Thakur³  Dipti Thakur³ 

[1] Informatics, University Politehnica of Bucharest, Bucharest, Romania;Department of Mathematics &School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, India

关键词: generalized nonexpansive mappings;    fixed points;    convergence theorem;    uniformly convex Banach space;    47H09;    47H10;   

DOI  :  10.1186/s13663-015-0397-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we prove strong and weak convergence theorems for a mapping defined on a bounded, closed and convex subset of a uniformly convex Banach space, satisfying the RCSC condition. This condition was introduced by Karapınar (Dynamical Systems and Methods, 2012). We first establish the demiclosed principle for the mapping satisfying the RCSC condition. Then, using this principle, we establish the weak and strong convergence theorems. Results in the paper extend and improve a number of important results in this literature such as Khan and Suzuki (Nonlinear Anal. 80:211-215, 2013) and Reich (J. Math. Anal. Appl. 67:274-276, 1979).

【 授权许可】

CC BY