Approximation for fixed points of strict pseudo-contractions and solutions of equilibrium and optimization problems

Abstract

In this paper, we introduce some iterative schemes for finding a common element of the set of fixed points of a k -strict pseudo-contractive mapping, the set of solutions of the variational inequality and the set of solutions of an equilibrium problem in a Hilbert space. The authors use the convex combination technique to show that the iterative sequences converge strongly to a common element of the three sets. The results of this paper extend and improve the results of Y. Su et al. [Nonlinear Anal: 2007], S. Plubtieng and R. Punpaeng [Appl. Math. Comput.: 2007], X. Qin et al. [Nonlinear Anal.: 2007] and S. Takahashi and W. Takahashi [J. Math. Anal. Appl. 331: 506–515, 2007].