Strong Convergence of a New Multi-Step Algorithm for Strict Pseudo-Contractive Mappings and Ky Fan Inequality

In this paper, we present a new multi-step algorithm for approximating a common element of the solution set of Ky Fan inequality and the set of common fixed points of a finite family of strict pseudo-contractive mappings in a real Hilbert space. This algorithm is based on Korpelevich’s extragradient method and viscosity approximation method. We prove a strong convergence theorem for the sequences generated by the algorithm. As applications, at the end of paper we utilize our results to study finding a common point of the solution set of an variational inequality problem and the fixed-point set of a finite family of strictly pseudo-contractive mappings. The results presented in this paper improve, extend, supplement and develop the corresponding results announced in the earlier and very recent literature.