Convergence of algorithms for fixed points of relatively nonexpansive mappings via Ishikawa iteration

Abstract

By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, 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.