**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}

^{a}Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

^{b}Department 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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