A new hybrid relaxed extragradient algorithm for solving equilibrium problems, variational inequalities and fixed point problems

Abstract

The purpose of this paper is to introduce a new hybrid relaxed extragradient iterative method for finding a common element of the solution of set a equilibrium, variational inequality and the set of fixed point of a-strict pseudocontraction mapping in Hilbert spaces. We obtain a strong convergence theorem of the purposed iterative algorithm under some suitable conditions. The results presented in this paper generalize, improve and extend some well-known results in the literature. © 2014 Springer Science+Business Media Dordrecht.