Accelerated Hybrid Mann-type Algorithm for Fixed Point and Variational Inequality Problems

Authors

Keywords:

Mann-type algorithm, inertial method, monotone operator, variational inequality problem, fixed point problem

Abstract

The purpose of this paper is to establish and study an accelerated hybrid Mann-type algorithm for the fixed point of nonexpansive mappings and variational inequality problems of monotone operators with the Lipschitz condition. Based on the Mann algorithm that generates a new iterative vector by a convex combination of the previous two iterative vectors, the advantageous behavior in the construction of a new iterative vector was observed due to the convex combination of three iterative vectors. Furthermore, by combining with the method known as the inertial Tseng’s extragradient method, the accelerated hybrid Mann-type algorithm was established. To demonstrate the efficiency and advantages of this new algorithm, we have created some numerical results to compare the advantages of different areas with the previous existing results.

Author Biographies

Purit Thammasiri, Department of Mathematics, Faculty of Science, Naresuan University

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

Kasamsuk Ungchittrakool, Department of Mathematics, Faculty of Science, Naresuan University

Associate Professor in Mathematics at Research Center for Academic Excellence in Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

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Published

2022-05-31

How to Cite

Thammasiri, P., & Ungchittrakool, K. (2022). Accelerated Hybrid Mann-type Algorithm for Fixed Point and Variational Inequality Problems. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 1(1), 97–111. Retrieved from https://bangmodjmcs.com/index.php/ncao/article/view/79

Issue

Vol. 1 No. 1 (2022): January - June, 2022

Section

Articles

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Copyright (c) 2022 Purit Thammasiri, Kasamsuk Ungchittrakool

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