A NOTE ON BEST PROXIMITY POINTS FOR $P$ SUMMING CYCLIC ORBITAL MEIR KEELER CONTRACTIONS
The classical Banach contraction theorem has a lot of applications [1] One of the interesting generalizations of Banach contraction is the well known Meir Keeler contraction theorem [12] In [3] the following notions are introduced.If A and B are non empty subsets of a metric space (X, d) and if T AB AB is such that T (A) T (B) and T (B) T (A) then T is called a cyclic map. A point x AB is called a best proximity point if d(x, Tx) dist(A,B) where dist(A,B) inf{d(x, y) x A and y B} In this paper a best proximity point is obtained for a map called cyclic contraction. It is further generalized in [2] by introducing a map called cyclic Meir Keeler contraction.