Abstract
The purpose of this paper is to introduce the modified Agarwal-O’Regan-Sahu iteration process (S-iteration) for finding endpoints of multivalued nonexpansive mappings in the setting of Banach spaces. Under suitable conditions, some weak and strong convergence results of the iterative sequence generated by the proposed process are proved. Our results especially improve and unify some recent results of Panyanak (J. Fixed Point Theory Appl. (2018)). At the end of the paper, we offer an example to illustrate the main results.
Highlights
Introduction and Preliminaries roughout this paper, N stands for the set of natural numbers, and R stands for the set of real numbers
For a multivalued mapping T: C ⟶ K(C), if q ∈ C is an endpoint of T, q is a fixed point of T; but the converse is not always true
Let xn be a sequence defined by (5). en, limn⟶∞‖xn − q‖ exists for each q ∈ ET
Summary
Introduction andPreliminaries roughout this paper, N stands for the set of natural numbers, and R stands for the set of real numbers. A multivalued mapping T: C ⟶ K(C) is said to satisfy the endpoint condition [1] if ET FT. Sastry and Babu [2] proved Mann and Ishikawa-type convergence results for multivalued nonexpansive mappings in the framework of Hilbert spaces.
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