Abstract
The purpose of this paper is to introduce modifying Halpern-Mann’s iterations sequence for a quasi-ϕ-asymptotically nonexpansive multi-valued mapping. Under suitable limit conditions, some strong convergence theorems are proved. The results presented in the paper improve and extend the corresponding results of Chang (Appl. Math. Comput. 218:6489-6497, 2012).
Highlights
Throughout this paper, we denote by N and R the sets of positive integers and real numbers, respectively
A mapping T : D → D is said to be nonexpansive if Tx – Ty ≤ x – y for all x, y ∈ D
Inspired by Matsushita and Takahashi, in this paper, we introduce modifying HalpernMann iterations sequence for finding a fixed point of a quasi-φ-nonexpansive mappings multi-valued mapping T : D → CB(D) and prove some strong convergence theorems
Summary
Throughout this paper, we denote by N and R the sets of positive integers and real numbers, respectively. Let D be a nonempty closed subset of a real Banach space X. (see [ ]) Let D be the generalized projection from a smooth, reflexive, and strictly convex Banach space X onto a nonempty closed convex subset D of X, D is closed and quasi-φ-nonexpansive from X onto D.
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