The Convergence of Three-Step Iterative Schemes for Generalized Φ − Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence

Abstract

Charles proved the convergence of Picard-type iteration for generalized $\mathrm{\Phi }-$ accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly $\mathrm{\Phi }-$ quasi-accretive mappings and fixed points of strongly $\mathrm{\Phi }-$ hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized $\mathrm{\Phi }-$ hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.