Generalized viscosity method for approximating solutions of countable families of certain nonlinear mappings in real Hilbert space

Abstract

The purpose of this paper is to introduce a three step iterative algorithm which include a general viscosity explicit method for approximating a common solution of fixed point problem of an infinite family of k_i-demimetric mapping and a directed operator in the framework of real Hilbert space. Furthermore, we prove a strong convergence theorem for approximating a common solution of the aforementioned problems. We also show that our iterative algorithm holds for an infinite family of L-Lipschitzian and quasi-pseudocontractive mapping together with a directed operator. The iterative algorithm presented in this article is design in such a way that it solves some variational inequality problem and no compactness condition is impose on our scheme and mapping. Finally, we give applications of our main result to variational inclusion and equilibrium problems. Our result complements and extends some related result in literature.