Double Inertial Krasnosel'skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings
Besheng George Akuchu, Uzoamaka A. Ezeafulukwe, Maggie Aphane, Godwin Chidi Ugwunnadi, Chukwuebuka Malachi Asanya · European Journal of Pure and Applied Mathematics · 2024
In this paper, we investigate a new method motivated by current advancements in general inertial algorithms. Specifically, we incorporate double inertial extrapolation terms into an iterative sequence, derived from Krasnosel'skii-Mann techniques. The weak convergence theorem for fixed points of nonexpansive mappings in real Hilbert spaces is established. The theoretical developments are rigorously proven, extending existing methods in literature. We also utilize our convergence analysis to solve real-world problems, such as convex minimization problems and zero finding for sums of monotone operators.