Inertial iterative method for a generalized mixed equilibrium, variational inequality and a fixed point problems for a family of quasi-$\phi$-nonexpansive mappings

Abstract

We introduce an inertial type gradient projection hybrid iterative method for finding a common solution of generalized mixed equilibrium, variational inequality and fixed point problems in a two-uniformly convex and uniformly smooth Banach space. Next, we analyze the strong convergence for a common solution of problem. Furthermore, we carry out some consequences and present a numerical example to show and tell the applicability of main theorem. Our result improves, unifies, generalizes and extends ones from several earlier works.