Document Type : Research Paper

Authors

1 Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.

2 Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.

Abstract

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 $T:C\rightarrow X$ 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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