One-local retracts and Banach operator pairs in metric spaces

N. Hussain; M. A. Khamsi; W. A. Kirk

doi:10.1016/j.amc.2012.03.067

One-local retracts and Banach operator pairs in metric spaces

N. Hussain, M. A. Khamsi, W. A. Kirk

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we first introduce the concept of NR-map and then use this concept to establish the existence of common fixed points for Banach operator pairs in the context of uniformly convex geodesic metric spaces. New proofs of main results (Theorems 2.1 and 3.5) of Chen and Li [J. Chen, Z. Li, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal. 74 (2011) 3086-3090] are presented. Further, we prove De Marr's theorem for the family of symmetric Banach operator pairs in metric spaces and R-trees for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity.

Original language	British English
Pages (from-to)	10072-10081
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	218
Issue number	20
DOIs	https://doi.org/10.1016/j.amc.2012.03.067
State	Published - 15 Jun 2012

Keywords

Banach operator pair
Fixed point
Hyperconvex metric space
Nearest point projection
Nonexpansive mapping

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title = "One-local retracts and Banach operator pairs in metric spaces",

abstract = "In this paper, we first introduce the concept of NR-map and then use this concept to establish the existence of common fixed points for Banach operator pairs in the context of uniformly convex geodesic metric spaces. New proofs of main results (Theorems 2.1 and 3.5) of Chen and Li [J. Chen, Z. Li, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal. 74 (2011) 3086-3090] are presented. Further, we prove De Marr's theorem for the family of symmetric Banach operator pairs in metric spaces and R-trees for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity.",

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note = "Funding Information: The first and second author gratefully acknowledge the financial support provided by University of Tabuk through the project of international cooperation. The authors thank the referee for his/her valuable suggestions to improve presentation of the paper. ",

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AU - Hussain, N.

AU - Khamsi, M. A.

AU - Kirk, W. A.

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N2 - In this paper, we first introduce the concept of NR-map and then use this concept to establish the existence of common fixed points for Banach operator pairs in the context of uniformly convex geodesic metric spaces. New proofs of main results (Theorems 2.1 and 3.5) of Chen and Li [J. Chen, Z. Li, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal. 74 (2011) 3086-3090] are presented. Further, we prove De Marr's theorem for the family of symmetric Banach operator pairs in metric spaces and R-trees for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity.

AB - In this paper, we first introduce the concept of NR-map and then use this concept to establish the existence of common fixed points for Banach operator pairs in the context of uniformly convex geodesic metric spaces. New proofs of main results (Theorems 2.1 and 3.5) of Chen and Li [J. Chen, Z. Li, Banach operator pair and common fixed points for nonexpansive maps, Nonlinear Anal. 74 (2011) 3086-3090] are presented. Further, we prove De Marr's theorem for the family of symmetric Banach operator pairs in metric spaces and R-trees for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity.

KW - Banach operator pair

KW - Fixed point

KW - Hyperconvex metric space

KW - Nearest point projection

KW - Nonexpansive mapping

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ER -

One-local retracts and Banach operator pairs in metric spaces

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