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:c→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.