Proximity Point Properties for Admitting Center Maps

Proximity Point Properties for Admitting Center Maps

In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T...

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Bibliographic Details
Main Authors: Mohammad Hosein Labbaf Ghasemi, Mohammad Reza Haddadi, Noha Eftekhari
Format: Article
Language:English
Published: University of Maragheh 2019-07-01
Series:Sahand Communications in Mathematical Analysis
Subjects:
‎Admitting center map
Nonexpansive map
Cochebyshev set
Best proximity pair
Online Access:http://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf
Description
Summary:In this work we investigate a class of admitting center maps on a metric space. We state and prove some fixed point and best proximity point theorems for them. We obtain some results and relevant examples. In particular, we show that if $X$ is a reflexive Banach space with the Opial condition and $T:Crightarrow X$ is a continuous admiting center map, then $T$ has a fixed point in $X.$ Also, we show that in some conditions, the set of all best proximity points is nonempty and compact.
ISSN:2322-5807
2423-3900

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