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...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
University of Maragheh
2019-07-01
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Series: | Sahand Communications in Mathematical Analysis |
Subjects: | |
Online Access: | http://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf |
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. |
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ISSN: | 2322-5807 2423-3900 |