Abstract

In this article, we propose a parallel viscosity iterative method for determining a common solution of a finite family of generalized equilibrium problems and a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problems and a fixed point problem for a nonexpansive mapping. We apply our result to solve a convex minimization problem and present a numerical example to demonstrate the performance of our method. Our results extend and improve many related results on generalized equilibrium problems from linear spaces to Hadamard manifolds.

Keywords: Generalized equilibrium problem; viscosity method; Hadamard manifold; monotone operator; Riemannian manifold.

MSC: 47J20, 47N10, 65B05, 47J26

DOI: 10.57016/MV-QP9476IM

Pages:  1--16