Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces

Khonchaliew, Manatchanok; Khamdam, Kunlanan; Petrot, Narin

doi:10.3390/sym16091099

Open AccessArticle

Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces

by

Manatchanok Khonchaliew

¹

,

Kunlanan Khamdam

² and

Narin Petrot

^2,3,*

¹

Department of Mathematics, Faculty of Science, Lampang Rajabhat University, Lampang 52100, Thailand

²

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

³

Centre of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

^*

Author to whom correspondence should be addressed.

Symmetry 2024, 16(9), 1099; https://doi.org/10.3390/sym16091099

Submission received: 16 July 2024 / Revised: 14 August 2024 / Accepted: 17 August 2024 / Published: 23 August 2024

(This article belongs to the Section B: Mathematics)

Download Versions Notes

Abstract

This paper presents the Mann-type inertial accelerated subgradient extragradient algorithm with non-monotonic step sizes for solving the split equilibrium and fixed point problems relating to pseudomonotone and Lipschitz-type continuous bifunctions and nonexpansive mappings in the framework of real Hilbert spaces. By sufficient conditions on the control sequences of the parameters of concern, the strong convergence theorem to support the proposed algorithm, which involves neither prior knowledge of the Lipschitz constants of bifunctions nor the operator norm of the bounded linear operator, is demonstrated. Some numerical experiments are performed to show the efficacy of the proposed algorithm.

Keywords: split equilibrium problems; split fixed point problems; pseudomonotone bifunction; nonexpansive mapping; subgradient extragradient method; inertial method

Share and Cite

MDPI and ACS Style

Khonchaliew, M.; Khamdam, K.; Petrot, N. Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces. Symmetry 2024, 16, 1099. https://doi.org/10.3390/sym16091099

AMA Style

Khonchaliew M, Khamdam K, Petrot N. Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces. Symmetry. 2024; 16(9):1099. https://doi.org/10.3390/sym16091099

Chicago/Turabian Style

Khonchaliew, Manatchanok, Kunlanan Khamdam, and Narin Petrot. 2024. "Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces" Symmetry 16, no. 9: 1099. https://doi.org/10.3390/sym16091099

APA Style

Khonchaliew, M., Khamdam, K., & Petrot, N. (2024). Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces. Symmetry, 16(9), 1099. https://doi.org/10.3390/sym16091099

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Mann-Type Inertial Accelerated Subgradient Extragradient Algorithm for Minimum-Norm Solution of Split Equilibrium Problems Induced by Fixed Point Problems in Hilbert Spaces

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI