Modified Iterative Algorithms for Nonexpansive Mappings

Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F(S)∩F(T)≠∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms fo...

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Vydáno v:International journal of stochastic analysis Ročník 2009; číslo 1
Hlavní autoři: Yao, Yonghong, Noor, Muhammad Aslam, Mohyud-Din, Syed Tauseef
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Hindawi Publishing Corporation 2009
Hindawi Limited
Témata:
Algorithms
Hilbert space
Iterative methods
Studies
ISSN:1048-9533, 2090-3332, 1687-2177, 2090-3340
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Shrnutí:Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F(S)∩F(T)≠∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. 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 xn+1=βnxn+(1−βn)Syn, yn=αnγf(xn)+(I−αnA)Txn, n≥0 is a real number and {αn}, {βn} are two sequences in (0,1) satisfying the following control conditions: (C1) lim n→∞ αn=0, (C3) 0<lim inf n→∞ βn≤lim sup n→∞ βn<1, then ∥xn+1−xn∥→0. We also discuss several special cases of this iterative algorithm.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1048-9533
2090-3332
1687-2177
2090-3340
DOI:10.1155/2009/320820