best proximity points for cyclic generalized contractions

in this paper we introduce cyclic generalized contraction maps and the theorems asked about it. moreover, we obtain existence and convergence of best proximity points for this mappings in uniformly convex banach space.

throughout this paper. we denote by n and r the sets of positive integers and real numbers, respectively. recently, the existence, uniqueness and convergence of iterates to the best proximity point were investigated by many authors; see [1-5,8-9]. in 2006, eldred and veeramani [4] first gave the concept of cyclic contraction as follows.

in this section, we shall state and prove some results about existence and convergence of best proximity points for cyclic generalized contraction maps in uniformly convex banach spaces.