文摘
Our purpose in this paper is to construct a new iterative scheme and prove strong convergence theorem using the iterative scheme for approximation of a common fixed point of a countable family of relatively nonexpansive mappings, which is also a solution to a finite system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space. We apply our results to approximate fixed point of a nonexpansive mapping, which is also solution to a finite system of equilibrium problems in a real Hilbert space, and approximate a common solution to finite system of variational inequality problems and convex minimization problems which is also a common solution to countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space. Our results extend many known recent results in the literature. Keywords Relatively nonexpansive mappings Generalized projection operator Equilibrium problem Banach spaces