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.
Highlights
In the early 1960s, Stampacchia [1] introduced the variational inequalities theory, which has emerged as an interesting branch of applied mathematics with a wide range of applications in industry, physics, optimization, social and science
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
Motivated and inspired by the work in the literature, 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
Summary
In the early 1960s, Stampacchia [1] introduced the variational inequalities theory, which has emerged as an interesting branch of applied mathematics with a wide range of applications in industry, physics, optimization, social and science. The theory of fixed points has grown rapidly into a flourishing and dynamic field of study both in pure and applied mathematics It has become one of the most essential tools in the study of nonlinear phenomena. The study for variational inequalities, fixed points and approximation algorithms became a topic of intensive research efforts in recent years. Nowadays, this is still one of the most active fields in mathematics. Motivated and inspired by the work in the literature, 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. The results are the extension and improvement of the recent results in the literature; see [9] [10] [11] [12]
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