TY - JOUR ID - 35727 TI - Proximity Point Properties for Admitting Center Maps JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Labbaf Ghasemi, Mohammad Hosein AU - Haddadi, Mohammad Reza AU - Eftekhari, Noha AD - Department of pure mathematics, Faculty of mathematical sciences, Shahrekord University, Shahrekord 88186-34141, Iran. AD - Faculty of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran. Y1 - 2019 PY - 2019 VL - 15 IS - 1 SP - 159 EP - 167 KW - ‎Admitting center map KW - Nonexpansive map KW - Cochebyshev set KW - Best proximity pair DO - 10.22130/scma.2018.79127.368 N2 - 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. UR - https://scma.maragheh.ac.ir/article_35727.html L1 - https://scma.maragheh.ac.ir/article_35727_15419203e3dc5caf276cf58d24d3fb14.pdf ER -