Existence and convergence theorems for the split quasi variational inequality problems on proximally smooth sets

Volume 9, Issue 5, pp 2364--2375 http://dx.doi.org/10.22436/jnsa.009.05.37

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Authors

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

Abstract

In this paper, we consider the split quasi variational inequality problems over a class of nonconvex sets, as uniformly prox-regular sets. The sufficient conditions for the existence of solutions of such a problem are provided. Furthermore, an iterative algorithm for finding a solution is constructed and its convergence analysis are considered. The results in this paper improve and extend the variational inequality problems which have been appeared in literature.

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Keywords

• Split quasi variational inequality
• proximally smooth set
• uniformly prox-regular set
• Lipschitzian mapping
• strongly monotone mapping.

MSC

•  49J40
•  47J20

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