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
Summary
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
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
