On the Best Proximity Points for <i>p</i>–Cyclic Summing Contractions

Abstract

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.

Keywords

• fixed point
• cyclical operator
• contractive condition
• best proximity point
• uniformly convex Banach space
• <i>p</i>–summing contraction