On a Viscosity Iterative Method for Solving Variational Inequality Problems in Hadamard Spaces

Abstract

In this paper, we propose and study an iterative algorithm that comprises of a finite family of inverse strongly monotone mappings and a finite family of Lipschitz demicontractive mappings in an Hadamard space. We establish that the proposed algorithm converges strongly to a common solution of a finite family of variational inequality problems, which is also a common fixed point of the demicontractive mappings. Furthermore, we provide a numerical experiment to demonstrate the applicability of our results. Our results generalize some recent results in literature.

Keywords

• variational inequalities
• inverse strongly monotone mappings
• demicontractive mappings
• fixed point problems
• Hadamard spaces