Double Inertial Krasnosel'skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings

Authors

  • Besheng George Akuchu University of Nigeria Nsukka, Nigeria
  • Uzoamaka Ezeafulukwe University of Nigeria Nsukka, Nigeria
  • Maggie Aphane Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria 0204, South Africa
  • Godwin Ugwunnadi University of Eswatini
  • Chukwuebuka Malachi Asanya University of Nigeria Nsukka, Nigeria

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i3.5327

Keywords:

Nonexpansive Mappings, common fixed points, Convergence Analysis, Inertial terms, Krasnosel'skii-Mann-Type Sequence

Abstract

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. 

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Published

2024-07-31

Issue

Vol. 17 No. 3: (July 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 European Journal of Pure and Applied Mathematics

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How to Cite

Double Inertial Krasnosel’skii-Mann-Type Method for Approximating Fixed Point of Nonexpansive Mappings. (2024). European Journal of Pure and Applied Mathematics, 17(3), 2246-2263. https://doi.org/10.29020/nybg.ejpam.v17i3.5327