Implicit iteration process of nonexpansive non-self-mappings

Somyot Plubtieng and Rattanaporn Punpaeng

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-8

Abstract:

Suppose C is a nonempty closed convex subset of real Hilbert space H . Let T : C → H be a nonexpansive non-self-mapping and P is the nearest point projection of H onto C . In this paper, we study the convergence of the sequences { x n } , { y n } , { z n } satisfying x n = ( 1 − α n ) u + α n T [ ( 1 − β n ) x n + β n T x n ] , y n = ( 1 − α n ) u + α n P T [ ( 1 − β n ) y n + β n P T y n ] , and z n = P [ ( 1 − α n ) u + α n T P [ ( 1 − β n ) z n + β n T z n ] ] , where { α n } ⊆ ( 0 , 1 ) , 0 ≤ β n ≤ β < 1 and α n → 1 as n → ∞ . Our results extend and improve the recent ones announced by Xu and Yin, and many others.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:630842

DOI: 10.1155/IJMMS.2005.3103

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