Novel Multistep Implicit Iterative Methods for Solving Common Solution Problems with Asymptotically Demicontractive Operators and Applications

Hai-Yang Xu and Heng-You Lan ()
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Hai-Yang Xu: College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
Heng-You Lan: College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China

Mathematics, 2023, vol. 11, issue 18, 1-20

Abstract: It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu’s lemma and Maingé’s fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations.

Keywords: strong convergence; common solution; asymptotically demicontractive operator system; novel multistep implicit iterative method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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