Fixed Point Methods and Optimization

Electronic ISSN: 3008-1548

DOI: 10.69829/fpmo

New general semi-implicit viscosity iterations with errors for approximating common fixed points of quasi-nonexpansive operators and applications

Fixed Point Methods and Optimization, Volume 2, Issue 1, April 2025, Pages 56–76

YAO YE

College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, 643000, Sichuan, PR China

DHENG-YOU LAN

Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong, 643000, Sichuan, PR China


Abstract

The purpose of this paper is to introduce and study a new class of general semi-implicit viscosity approximation methods involving inaccurate computation errors and quasi-nonexpansive operators in Hilbert spaces. We also analyze convergence of the new iterative approximations for common fixed points of three different quasi-nonexpansive operators, which are also the unique solutions of a variational inequality. Furthermore, we present numerical examples to verify the main results presented in this paper. As applications, we investigate a class of split equality fixed point problems and split equality common fixed point problems.


Cite this Article as

Yao Ye and Heng-You Lan, Generalized split zero point problems involving comonotone and quasi-cocoercive operators, Fixed Point Methods and Optimization, 2(1), 56–76, 2025