A neural network for solving the generalized inverse mixed variational inequality problem in Hilbert Spaces

Jittiporn Tangkhawiwetkul; Jittiporn Tangkhawiwetkul

doi:10.3934/math.2023365

AIMS Mathematics

2023, Volume 8, Issue 3: 7258-7276. doi: 10.3934/math.2023365

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A neural network for solving the generalized inverse mixed variational inequality problem in Hilbert Spaces

Jittiporn Tangkhawiwetkul ^,

Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok, 65000, Thailand

Received: 29 September 2022 Revised: 05 December 2022 Accepted: 06 December 2022 Published: 12 January 2023
MSC : 49J40, 65P40

In this paper, we study and analyze the generalized inverse mixed variational inequality. The existence and uniqueness of the solution of such problem are proposed. The neural network associated with the generalized inverse mixed variational inequality is presented, and moreover, the Wiener-Hopf equation which the solution of the equation is equivalent to the solution of the generalized inverse mixed variational inequality, is considered. The stability and existence of solution of such neural network are proved. Finally, we introduce some algorithms which are constructed by the concept of the neural network and display a numerical example for understanding our results.
- generalized $ f $-projection operator,
- generalized inverse mixed variational inequality,
- Wiener-Hopf equation,
- neural network,
- equilibrium point
Citation: Jittiporn Tangkhawiwetkul. A neural network for solving the generalized inverse mixed variational inequality problem in Hilbert Spaces[J]. AIMS Mathematics, 2023, 8(3): 7258-7276. doi: 10.3934/math.2023365

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Abstract

In this paper, we study and analyze the generalized inverse mixed variational inequality. The existence and uniqueness of the solution of such problem are proposed. The neural network associated with the generalized inverse mixed variational inequality is presented, and moreover, the Wiener-Hopf equation which the solution of the equation is equivalent to the solution of the generalized inverse mixed variational inequality, is considered. The stability and existence of solution of such neural network are proved. Finally, we introduce some algorithms which are constructed by the concept of the neural network and display a numerical example for understanding our results.

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