An inertial extragradient algorithm for a common solution of generalized mixed equilibrium problem and fixed point problem of nonexpansive mappings

In this paper, we propose an inertial iterative method for approximating a common solution of generalized mixed equilibrium problem for monotone and uniformly continuous operators and fixed point of nonexpansive mapping in real Hilbert space. The strong convergence of the sequence generated by the proposed method can be guaranteed without prior knowledge of the Lipschitz constant of the operator. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method. Our result improves, extends and generalizes several of the existing results in this direction.