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

TL;DR

This paper demonstrates that the Ishikawa iterative algorithm effectively approximates fixed points of relatively nonexpansive mappings in Hilbert spaces, showing faster convergence than some existing methods through theoretical proofs and numerical comparisons.

Contribution

The paper introduces convergence results for Ishikawa iteration applied to relatively nonexpansive mappings and compares its efficiency with other algorithms using numerical examples.

Findings

Ishikawa iteration converges faster than Picard and Mann iterations.

The convergence is established using von Neumann sequences in Hilbert spaces.

Numerical results confirm the theoretical advantages of 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.