University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Proximity Point Properties for Admitting Center Maps1591673572710.22130/scma.2018.79127.368ENMohammad HoseinLabbaf GhasemiDepartment of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.Mohammad RezaHaddadiFaculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran.NohaEftekhariDepartment of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran.0000-0002-8159-1652Journal Article20180119In 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.https://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf