Abstract
Abstract In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings and utilize the same to prove some convergence theorems. In the process, we remove a restricted condition (called end-point condition) in Sokhuma and Kaewkhao’s results (Fixed Point Theory Appl. 2010:618767, 2010). Thus, our results generalized and improved several results contained in Sokhuma and Kaewkhao (Fixed Point Theory Appl. 2010:618767, 2010), Akkasriworn et al. (Int. J. Math. Anal. 6(19):923-932, 2012), Uddin et al. (Bull. Malays. Math. Soc., accepted) and Sokhuma (J. Math. Anal. 4(2):23-31, 2013). MSC:47H10, 54H25.
Highlights
Let X be a Banach space and K be a nonempty subset of X
It is well known that every closed convex subset of a uniformly convex Banach space is proximinal
With a motivation to remove this strong condition, in this paper we introduce a new iteration scheme for a pair of hybrid mapping and prove some convergence theorems for generalized nonexpansive mappings
Summary
Let X be a Banach space and K be a nonempty subset of X.
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