The new variational inclusion problems for fixed point theorem

Abstract

For the purpose of this article, we modify the variational inclusion problems and prove the strong convergence theorem for approximating a common element of two sets of solutions of variational inclusion problems, variational inequality problem and the set of fixed points of a nonexpansive mapping without the conditions ∑n=l∞ αn = ∞ and limn→∞αn = 0 in a framework of Hilbert space.