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On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces.
- Source :
- Carpathian Journal of Mathematics; 2021, Vol. 37 Issue 3, p513-527, 15p
- Publication Year :
- 2021
-
Abstract
- We prove Δ-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. [ABSTRACT FROM AUTHOR]
- Subjects :
- SET-valued maps
METRIC spaces
FIXED point theory
Subjects
Details
- Language :
- English
- ISSN :
- 15842851
- Volume :
- 37
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Carpathian Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 151392631
- Full Text :
- https://doi.org/10.37193/CJM.2021.03.13