An Ishikawa-Hybrid Proximal Point Algorithm for Nonlinear Set-Valued Inclusions Problem Based on (A,η)-Accretive Framework

Abstract

A general nonlinear framework for an Ishikawa-hybrid proximal point algorithm using the notion of (A,η)-accretive is developed. Convergence analysis for the algorithm of solving a nonlinear set-valued inclusions problem and existence analysis of solution for the nonlinear set-valued inclusions problem are explored along with some results on the resolvent operator corresponding to (A,η)-accretive mapping due to Lan-Cho-Verma in Banach space. The result that sequence {xn} generated by the algorithm converges linearly to a solution of the nonlinear set-valued inclusions problem with the convergence rate θ is proved.