Best proximity point theorems for probabilistic proximal cyclic contraction with applications in nonlinear programming

Abstract In this paper, we derive a best proximity point theorem for non-self-mappings satisfied proximal cyclic contraction in PM-spaces and this shows the existence of optimal approximate solutions of certain simultaneous fixed point equations in the event that there is no solution. As an application we consider a nonlinear programming problem. Our results extend and improve the recent results of (Sadiq Basha in Nonlinear Anal. 74(17):5844-5850, 2011).