Abstract

In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.

Highlights

  • The theory of variational inequality provides a natural and elegant framework for study of many seemingly unrelated free boundary value problems arising in various branches of engineering and mathematical sciences

  • We propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions

  • We prove the existence and convergence of random iterative sequences generated by random iterative algorithms

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Summary

Introduction

The theory of variational inequality provides a natural and elegant framework for study of many seemingly unrelated free boundary value problems arising in various branches of engineering and mathematical sciences. Variational inequalities have many deep results dealing with nonlinear partial differential equations which play important and fundamental role in general equilibrium theory, economics, management sciences and operations research, see [1,2,3]. The quasi variational inequalities have been introduced by Bensoussan and Lions [1] and closely related to contact problems with friction in electrostatics and nonlinear random equations frequently arise in biological, physical and system sciences [4,5]. Motivated by recent research work on random variational inequalities [9,10,11,12,13,14], in this paper we consider a class of set valued nonlinear random implicit quasi variational inclusions and a class of random proximal operator equations and establish an equivalence between them. Further we prove the existence of solution of this class of problem and discuss the convergence of iterative sequences generated by these random iterative algorithms

Preliminaries
Random Iterative Algorithm
Main Result

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