Communications of the
Korean Mathematical Society CKMS

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also 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 problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

Keywords: Generalized equilibrium problem, shrinking method, Hadamard manifold, monotone operator, Riemannian manifold

MSC numbers: Primary 47H09, 49J25, 65K10, 90C25