Hybrid iterative scheme for fixed point problem, infinite systems of equilibrium and variational inequality problems

The purpose of this paper is to construct a new iterative scheme by the hybrid method and prove a strong convergence theorem for the approximation of a common fixed point of two countable families of weak relatively 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 Kadec–Klee property using the properties of a generalized ff-projection operator. Using this result, we give some applications. Our results extend many known recent results in the literature.