Inertial Tseng Method for Solving the Variational Inequality Problem and Monotone Inclusion Problem in Real Hilbert Space

Shamshad Husain, Mohammed Ahmed Osman Tom, Mubashshir U. Khairoowala, Mohd Furkan () and Faizan Ahmad Khan ()
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Shamshad Husain: Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
Mohammed Ahmed Osman Tom: Computational and Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
Mubashshir U. Khairoowala: Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
Mohd Furkan: University Polytechnic, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh 202002, India
Faizan Ahmad Khan: Computational and Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2022, vol. 10, issue 17, 1-16

Abstract: The main aim of this research is to introduce and investigate an inertial Tseng iterative method to approximate a common solution for the variational inequality problem for γ -inverse strongly monotone mapping and monotone inclusion problem in real Hilbert spaces. We establish a strong convergence theorem for our suggested iterative method to approximate a common solution for our proposed problems under some certain mild conditions. Furthermore, we deduce a consequence from the main convergence result. Finally, a numerical experiment is presented to demonstrate the effectiveness of the iterative method. The method and methodology described in this paper extend and unify previously published findings in this field.

Keywords: variational inequality problem; monotone inclusion problem; strong convergence; tseng iterative method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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