On Mann-type iteration method for a family of hemicontractive mappings in Hilbert spaces

Abstract

Let K be a compact convex subset of a real Hilbert space H and T i : K →K, i = 1,2, . . . , k, be a family of continuous hemicontractive mappings. Let αn,βni ∈ [0, 1] be such that αn + Σik =1 βni = 1 and satisfying {αn},β ni ⊂ [δ, 1 - δ] for some δ ∈ (0, 1), i = 1,2, . . . , k. For arbitrary x0 ∈ K, define the sequence {xn} by (1.9) see below, then {xn} converges strongly to a common fixed point in ∩ i=1k F(Ti) ≠ ∅. © 2013 Hussain et al.; licensee Springer.