The Dynamical System for System of Variational Inequality Problem in Hilbert Spaces

Authors

  • Narin Petrot Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000
  • Jittiporn Tangkhawiwetkul Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, 65000

DOI:

https://doi.org/10.26713/cma.v9i4.1105

Keywords:

Dynamical system, The system of variational inequality, Lipschitz mapping, Lyapunov's stability theorem, Gronwall's Lemma

Abstract

In this paper, we will present a dynamical system which relates to the system of variational inequality problem by starting with introducing a Wiener-Hopf equation for the system of variational inequality problem and using a such Wiener-Hopf equation for proposing a dynamical system for the system of variational inequality problem. Moreover, the existence solution of such dynamical system is considered and the stability, globally asymptotically stable and also globally exponential convergence, of the solution for the system of a such dynamical system are proved. The results in this paper improve and extend the variational inequality problems which have been appeared in literature.

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Published

25-12-2018
CITATION

How to Cite

Petrot, N., & Tangkhawiwetkul, J. (2018). The Dynamical System for System of Variational Inequality Problem in Hilbert Spaces. Communications in Mathematics and Applications, 9(4), 541–558. https://doi.org/10.26713/cma.v9i4.1105

Issue

Vol. 9 No. 4 (2018)

Section

Research Article

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