Inertial hybrid self-adaptive subgradient extragradient method for fixed point of quasi$-\phi-$nonexpansive multivalued mappings and equilibrium problem

Abstract

In this paper, we propose a new inertial self-adaptive subgradient extragradient algorithm for approximating common solution in the set of pseudomonotone equilibrium problems and the set of xed point of nite family of quasi−φ−nonexpansive multivalued mappings in real uniformly convex Banach spaces and uniformly smooth Banach spaces. Strong convergence of the iterative scheme is established. Our results generalizes and improves several recent results annouced in the literature.