A Halpern Resolvent-Subgradient-Extragradients Method for finding common solution of fixed point, h-fixed point, equilibrium and variational inequality problems in Banach spaces

The key idea behind solving well known applicable problems is to reformulate the problems as finding a fixed point of a suitably defined mapping. The theory of variational inequalities and equilibrium problems involving some operators with monotonicity conditions have received remarkable development with several methods suggested for solving them. Efforts have significantly been made in approximating fixed points and h-fixed point of (possibly set valued, nonlinear) mapping in different suitable real Banach spaces. The intersections of these four streams; functional-analytic fixed and h- fixed point theories, and the mathematics of variational and equilibrium problems have not been well researched. The purpose of this paper is to construct an algorithm for the approximation of the common solution of the set of h-fixed points of a h-pseudo-contractive mapping; set of fixed point of a Bregman quasi mapping; set of solution of equilibrium problems for pseudomonotone mapping and the set of variational inequality problem for Lipschitz monotone mapping which leads to a prove of strong convergence theorem for it in Banach spaces.