On the existence and approximation of solutions of generalized equilibrium problem on Hadamard manifolds

Abstract In this paper, we study the existence of solution generalized equilibrium problem (GEP) in framework an Hadamard manifold. Using KKM lemma, prove GEP and give properties resolvent function associated with under consideration. Furthermore, introduce iterative algorithm for approximating a common fixed point problem. proposed method, obtain strong convergence theorem GEP, which is also nonexpansive mapping some mild conditions. We application our result to convex minimization To illustrate report numerical experiments. The paper extends from linear settings manifolds.