Modified Iterative Algorithms for Nonexpansive Mappings

Yonghong Yao, Muhammad Aslam Noor and Syed Tauseef Mohyud-Din

International Journal of Stochastic Analysis, 2009, vol. 2009, 1-11

Abstract:

Let ð » be a real Hilbert space, let 𠑆 , 𠑇 be two nonexpansive mappings such that ð ¹ ( 𠑆 ) ∩ ð ¹ ( 𠑇 ) ≠∅ , let ð ‘“ be a contractive mapping, and let ð ´ be a strongly positive linear bounded operator on ð » . In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as ð ‘¥ ð ‘› + 1 = ð ›½ ð ‘› ð ‘¥ ð ‘› + ( 1 − ð ›½ ð ‘› ) 𠑆 𠑦 ð ‘› , 𠑦 ð ‘› = ð ›¼ ð ‘› ð ›¾ ð ‘“ ( ð ‘¥ ð ‘› ) + ( ð ¼ âˆ’ ð ›¼ ð ‘› ð ´ ) 𠑇 ð ‘¥ ð ‘› , ð ‘› ≥ 0 is a real number and { ð ›¼ ð ‘› } , { ð ›½ ð ‘› } are two sequences in ( 0 , 1 ) satisfying the following control conditions: (C1) l i m ð ‘› → ∞ ð ›¼ ð ‘› = 0 , (C3) 0 < l i m i n f ð ‘› → ∞ ð ›½ ð ‘› ≤ l i m s u p ð ‘› → ∞ ð ›½ ð ‘› < 1 , then ‖ ð ‘¥ ð ‘› + 1 − ð ‘¥ ð ‘› ‖ → 0 . We also discuss several special cases of this iterative algorithm.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:320820

DOI: 10.1155/2009/320820

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