On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces
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Published:2021-07-15
Issue:3
Volume:37
Page:513-527
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ISSN:1584-2851
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Container-title:Carpathian Journal of Mathematics
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language:
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Short-container-title:CJM
Author:
PUIWONG JENJIRA, ,SAEJUNG SATIT, ,
Abstract
We prove ∆-convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in p-uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the (CN) inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.
Publisher
Technical University of Cluj Napoca, North University Center of Baia Mare
Subject
General Mathematics
Cited by
1 articles.
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