Self-adaptive forward–backward splitting algorithm for the sum of two monotone operators in Banach spaces-Reference-Cited by-同舟云学术

Self-adaptive forward–backward splitting algorithm for the sum of two monotone operators in Banach spaces

Published:2022-12-06 Issue:1 Volume:2022 Page:
ISSN:2730-5422
Container-title:Fixed Point Theory and Algorithms for Sciences and Engineering
language:en
Short-container-title:Fixed Point Theory Algorithms Sci Eng

Author:

Bello Abdulmalik U.^ORCID,Chidume Charles E.,Alka Maryam

Abstract

AbstractIn this work, we prove the weak convergence of a one-step self-adaptive algorithm to a solution of the sum of two monotone operators in 2-uniformly convex and uniformly smooth real Banach spaces. We give numerical examples in infinite-dimensional spaces to compare our result with some existing algorithms. Finally, our results extend and complement several existing results in the literature.

Funder

African Development Bank Group

Publisher

Springer Science and Business Media LLC

Subject

Pharmacology (medical)

Link

https://link.springer.com/content/pdf/10.1186/s13663-022-00732-9.pdf

Reference30 articles.

1. Abass, H.A., Aremu, K.O., Jolaoso, L.O., Mewomo, O.T.: An inertial forward–backward splitting method for approximating solutions of certain optimization problems. J. Nonlinear Funct. Anal. 2020, Article ID 6 (2020)

2. Lecture Notes in Pure and Appl. Math.;Y. Alber,1996

3. Alber, Y., Guerre-Delabriere, S.: On the projections for fixed points problems. Analysis 21(1), 17–39 (2001)

4. Alber, Y., Ryazantseva, I.: Nonlinear Ill Posed Problems of Monotone Type. Springer, London (2006)

5. Aoyama, K., Kohsaka, F.: Strongly relatively nonexpansive sequences generated by firmly nonexpansive-like mappings. Fixed Point Theory Appl. 2014, Article ID 95 (2014)