Weak proximal normal structure and coincidence quasi-best proximity points

Farhad Fouladi; Ali Abkar; Erdal Karapinar

doi:10.4995/agt.2020.13926

Authors

Farhad Fouladi Imam Khomeini International University
Ali Abkar Imam Khomeini International University
Erdal Karapinar Thu Dau Mot University https://orcid.org/0000-0002-6798-3254

DOI:

https://doi.org/10.4995/agt.2020.13926

Keywords:

pointwise cyclic-noncyclic pairs, weak proximal normal structure, coincidence quasi-best proximity point

Abstract

We introduce the notion of pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. We study the best proximity point problem for this class of mappings. We also study the same problem for the class of pointwise noncyclic-noncyclic relatively nonexpansive pairs involving orbits. Finally, under the assumption of weak proximal normal structure, we prove a coincidence quasi-best proximity point theorem for pointwise cyclic-noncyclic relatively nonexpansive pairs involving orbits. Examples are provided to illustrate the observed results.

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Author Biographies

Farhad Fouladi, Imam Khomeini International University

Department of Pure Mathemathics,Faculty of Science

Ali Abkar, Imam Khomeini International University

Department of Pure Mathemathics, Faculty of Science

Erdal Karapinar, Thu Dau Mot University

ETSI Division of Applied Mathematics

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