Iterative approximation for common solutions of equilibrium problems, variational inequality and fixed point problems

Our purpose in this paper is to construct a new iterative scheme by the hybrid method and prove the strong convergence theorem using our new iterative scheme for approximation of a common fixed point of a countable family of uniformly quasi‐ $\phi$ ‐asymptotically nonexpansive mappings which is also a common solution to infinite systems of equilibrium and variational inequality problems in a uniformly smooth and strictly convex real Banach space with the Kadec–Klee property using the properties of the generalized $f$ ‐projection operator. Our results extend many known recent results in the literature.