ISHIKAWA ITERATION WITH ERRORS FOR APPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS OF BROWDER-PETRYSHYN TYPE

Abstract

Let q > 1 and E be a real q−uniformly smooth Banach space. Let K be a nonempty closed convex subset of E and T : K → K be a strictly pseudocontractive mapping in the sense of F. E. Browder and W. V. Petryshyn [1]. Let {un} be a bounded sequence in K and {αn}, {βn}, {γn} be real sequences in [0,1] satisfying some restrictions. Let {xn} be the bounded sequence in K generated from any given x1 ∈ K by the Ishikawa iteration method with errors: yn = (1 − βn)xn + βnTxn, xn+1 = (1 −αn − γn)xn + αnTyn + γnun, n ≥ 1. It is shown in this paper that if T is compact or demicompact, then {xn} converges strongly to a fixed point of T.