Convergence of Fixed Points for Relatively Nonexpansive Mappings via Ishikawa Iteration

Abstract

By using the Ishikawa iterative algorithm, we approximate fixed points and best proximity points of a relatively nonexpansive mapping. Furthermore, we use the von Neumann sequence to prove the convergence result in a Hilbert space setting. A comparison table is prepared using a numerical example which shows that the Ishikawa iterative algorithm is faster than some known iterative algorithms such as Picard and Mann iteration.