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

Abstract

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 α n , β n i ∈ [ 0 , 1 ] be such that α n + ∑ i = 1 k β n i = 1 and satisfying { α n } , β n i ⊂ [ δ , 1 − δ ] for some δ ∈ ( 0 , 1 ) , i = 1 , 2 , … , k . For arbitrary x 0 ∈ K , define the sequence { x n } by (1.9) see below, then { x n } converges strongly to a common fixed point in ⋂ i = 1 k F ( T i ) ≠ ∅ . MSC:05C38, 15A15, 05A15, 15A18.