Abstract
Abstract In this article, an iterative sequence for relatively nonexpansive multi-valued mapping by modifying Halpern and Mann's iterations is introduced, and then some strong convergence theorems are proved. At the end of the article some applications are given also. AMS Subject Classification: 47H09; 47H10; 49J25.
Highlights
Throughout this article, we denote by N and R the sets of positive integers and real numbers, respectively
A single-valued mapping T : D ® D is called nonexpansive if ∥Tx - Ty∥ ≤ ∥x - y∥ for all x, y Î D
In this article, inspired by Nilsrakoo and Saejung [7], we introduce the following iterative sequence for finding a fixed point of relatively nonexpansive multi-valued mapping T : D ® N(D)
Summary
Throughout this article, we denote by N and R the sets of positive integers and real numbers, respectively. ΑnJu + (1 − αn) βnJxn + (1 − βn)JTxn where D is nonempty closed convex subset of a uniformly convex and uniformly smooth Banach space E, ΠD is the generalized projection of E onto D and {an} and {bn} are two sequences in [0,1].
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