A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings
Uamporn Witthayarat, Jong Kyu Kim, Poom Kumam · Journal of Inequalities and Applications · 2012
Abstract 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.