Article ID: MTJPAM-D-21-00048

Title: Iterative algorithms for solving nonlinear quasi-variational inequalities


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00048; Volume 4 / Issue 1 / Year 2022, Pages 44-58

Document Type: Research Paper

Author(s): Muhammad Aslam Noor a , Khalida Inayat Noor b

aDepartment of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

bDepartment of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 18 July 2021, Accepted: 7 September 2021, Published: 5 October 2021.

Corresponding Author: Muhammad Aslam Noor (Email address: noormaslam@gmail.com)

Full Text: PDF

Abstract

In this paper, we consider the quasi-variational inequalities. It is shown that quasi-variational inequalities are equivalent to the implicit fixed point problems. Some new iterative methods for solving quasi-variational inequalities and related optimization problems are suggested by using projection methods, Wiener-Hopf equations and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under monotonicity. Some special cases are discussed as applications of the main results.

Keywords: Variational inequalities, projection method, Wiener-Hopf equations, dynamical system, convergence, applications

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