Error Estimates for Approximating Best Proximity Points for Cyclic Contractive Maps

TL;DR

This paper derives error estimates and convergence rates for approximating best proximity points in cyclic contraction maps within uniformly convex Banach spaces, enhancing understanding of iterative methods in this context.

Contribution

It provides new a priori and a posteriori error bounds and convergence rates for Picard iterations in cyclic contraction mappings on uniformly convex Banach spaces.

Findings

Derived explicit error estimates for best proximity point approximations.

Established convergence rates for Picard iteration sequences.

Applied results to uniformly convex Banach spaces with power type modulus.

Abstract

We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type. We find the rate of convergence for the Picard sequence.