A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces

In this work, we consider a general composite iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of fixed points, which solves the variational inequality 〈 ( γ f − μ F ) q , p − q 〉 ≤ 0 , for p ∈ ∩ i = 1 ∞ F ( T i ) . Our results improve and extend corresponding ones announced by many others.