Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold

Abstract

Abstract In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.

Keywords

• Equilibrium problem
• Nonexpansive mapping
• Fixed point problems
• Viscosity
• Hadamard manifold and extragradient algorithm