A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings

摘要

Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly pseudo-contractive mappings which solves the variational inequality 〈 ( γ f ? μ F ) q , p ? q 〉 ≤ 0 for p ∈ ? i = 1 ∞ F ( T i ) . Furthermore, we also prove the strong convergence theorems for the proposed iterative scheme and give a numerical example to support and illustrate our main theorem. MSC:46C05, 47D03, 47H05,47H09, 47H10, 47H20.