TITLE:
A Modified Thakur Three-Step Iterative Algorithm to Garcia-Falset Mappings and Variational Inequalities
AUTHORS:
Xinhong Chen, Wenxiang Han, Liping Gong, Chengjun Luo
KEYWORDS:
Banach Space, Fixed Point, Garcia-Falset Mapping, Strong Convergence, Variational Inequality
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.12,
December
21,
2020
ABSTRACT: In this paper, we suggest and analyze a modified Thakur three-step iterative algorithm to approximate a common element of the set of common fixed points of Garcia-Falset mappings and the set of solutions of some variational inequalities in Banach spaces. We also establish strong convergence theorems for a common solution of the above-said problems by the proposed iterative algorithm without the compactness assumption. The methods in this paper are novel and different from those given in many other papers. And the results are the extension and improvement of the recent results announced by many others.