Quasi Variational Inclusions Involving Three Operators

Authors

Muhammad Aslam Noor, Department of Mathematics, COMSATS University Islamabad, Islamabad, PakistanFollow
Khalida Inayat Noor, Department of Mathematics, COMSATS University Islamabad, Islamabad, PakistanFollow
Muhammad Uzair Awan, Department of Mathematics, Government College University, Faisalabad, PakistanFollow
Awais Gul Khan, Department of Mathematics, Government College University, Faisalabad, PakistanFollow

Abstract

In this paper, we consider some new classes of the quasi-variational inclusions involving three monotone operators. Some interesting problems such as variational inclusions involving sum of two monotone operators, difference of two monotone operators, system of absolute value equations, hemivariational inequalities and variational inequalities are the special cases of quasi variational inequalities. It is shown that quasi-variational inclusions are equivalent to the implicit fixed point problems. Some new iterative methods for solving quasi-variational inclusions and related optimization problems are suggested by using resolvent methods, resolvent 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.

Recommended Citation

Aslam Noor, Muhammad; Inayat Noor, Khalida; Uzair Awan, Muhammad; and Gul Khan, Awais (2022) "Quasi Variational Inclusions Involving Three Operators," Information Sciences Letters: Vol. 11 : Iss. 2 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol11/iss2/28