STRONG CONVERGENCE FOR HYBRID IMPLICIT S-ITERATION SCHEME OF NONEXPANSIVE AND ASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS

摘要

Let C be a non-empty closed convex subset of real Banach space E. Let S : C → C be non-expansive mapping and let T : C → C be a uniformly L-Lipschitizian, asymptotically demicontractive mapping with sequence {a_n} ⊆ [0, 1), lim_(n→∞) a_n = 1 such that || x - Sy || ≤ || Sx - Sy || and || x - Ty || ≤ || Tx - Ty> || ∨x, y ∈ C. Assume that F(S) ∩ F(T) = {x∈ C/Sx = Tx = x} ≠ Ø. Let p ∈ F(S) ∩ F(T) and {a_n} be a sequence in [0, 1] satisfying (i) Σ_(n=1)~∞ a_n = ∞, (ii) lim a_n = 0. For arbitrary x_1∈ C, let {x_n} be a sequence iteratively defined by x_(n+1) = Sy_n, y_n = (1 - a_n)x_n + a_nT~nx_n, n≥1. Then we prove that the sequence {x_n} converges strongly at the common fixed point p of Sand T.