Convergence of a Multi-Inertial-Iteration Scheme in Cone b, p-Normed Banach Spaces

TL;DR

This paper introduces a new multi-inertial iteration scheme in cone b, p-normed Banach spaces that extends classical methods, incorporating multiple parameters and error controls, with proven convergence and faster results.

Contribution

It develops a novel multi-inertial iteration framework that generalizes existing fixed point algorithms in cone p-normed Banach spaces with convergence guarantees.

Findings

Proven convergence under mild assumptions.

Numerical examples show accelerated convergence.

Extension of classical Krasnoselskii-Mann method.

Abstract

We propose and analyze a multi-inertial-iteration scheme in cone b, p-normed Banach spaces. This framework extends the classical Krasnoselskii-Mann and two-step inertial iterations by incorporating three independent inertial parameters and multiple error-control sequences. Under mild assumptions such as quasi-nonexpansiveness, weak contraction, and compatibility of mappings, we establish convergence theorems guaranteeing the existence and uniqueness of fixed points. Illustrative numerical examples demonstrate accelerated convergence compared with the classical Krasnoselskii-Mann method.