Convergence theorems for generalized nonexpansive mappings in uniformly convex Banach spaces

被引：0
|
作者：
Dipti Thakur
Balwant Singh Thakur
Mihai Postolache
机构：
[1] Pt. Ravishankar Shukla University,School of Studies in Mathematics
[2] University Politehnica of Bucharest,Department of Mathematics & Informatics
来源：
Fixed Point Theory and Applications | / 2015卷
关键词：
generalized nonexpansive mappings; fixed points; convergence theorem; uniformly convex Banach space; 47H09; 47H10;
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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).
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