A Strongly Convergent Algorithm for Approximating a Common Solution to Fixed Point and Mixed Equilibrium Problems

Abstract In this paper, we propose an inertial iterative method for solving a common solution to the fixed point and mixed equilibrium problem in Hilbert spaces. We prove the sequence generated by the proposed algorithm strongly converges to an element in the solution set of mixed equilibrium problems of a pair of bi-function, which is also the solution to a fixed point of demicontractive mapping. Finally, we give some numerical experiments to support our main result. Our result extends and generalizes some earlier announced results in the literature.