A new relaxed inertial Ishikawa-type algorithm for solving fixed points problems with applications to convex optimization problems

Abstract

In this research, we present a new relaxed intertial algorithm without viscosity for solving common solution of countable family of nonexpansive mappings in real Hilbert spaces. We obtain the strong convergence results of the proposed method under some wild conditions on the control parameters. Weapply our main results to solve convex bilevel optimization problems. Finally, we present a numerical example to illustrate the efficiency of our method over some existing methods in the literature.