Almost sure T-stability and convergence for random iterative algorithms
The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed p...
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| Published in | Applied mathematics and mechanics Vol. 32; no. 6; pp. 805 - 810 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Shanghai University Press
01.06.2011
Department of Mathematics, Yibin University, Yibin 644007, Sichuan Province, P. R. China |
| Subjects | |
| Online Access | Get full text |
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| Abstract | The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved. |
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| AbstractList | O177.91; The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of φ-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved. The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved. The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of Delta *q-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved. The purpose of this paper is to study the almost sure T -stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of ϕ -weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T -stability and convergence for these two kinds of random iterative algorithms are proved. |
| Author | 张石生 王雄瑞 刘敏 朱浸华 |
| AuthorAffiliation | Department of Mathematics, Yibin University, Yibin 644007, Sichuan Province, P. R. China |
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| Cites_doi | 10.1081/SAP-200044432 10.1016/S0362-546X(01)00388-1 10.1016/0022-247X(79)90023-4 10.21136/CMJ.1955.100162 10.1090/S0002-9947-1974-0348565-1 10.1007/978-3-0348-8910-0_2 |
| ClassificationCodes | O177.91 |
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| Copyright | Shanghai University and Springer-Verlag Berlin Heidelberg 2011 Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | separable Banach space Ishikawa-type random iterative scheme Mann-type random iterative scheme almost sure 47H09 49M05 Bochner integrability 47H05 stability O177.91 54H25 almost sure T-stability |
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| Notes | almost sure T-stability, separable Banach space, Bochner integrability,Ishikawa-type random iterative scheme, Mann-type random iterative scheme 31-1650/O1 The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved. ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| PublicationTitle | Applied mathematics and mechanics |
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| Publisher | Shanghai University Press Department of Mathematics, Yibin University, Yibin 644007, Sichuan Province, P. R. China |
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| References | ŠpačekA.Zufallige gleichungenCzechoslovak Mathematical Journal1955546246679854 ChangS. S.ChoY. J.KimJ. K.ZhouH. Y.Random Ishikawa iterative sequence with applicationsStochastic Analysis and Applications200523697721239441065.6008410.1081/SAP-200044432 HansO.Random operator equationsProceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability1961CaliforniaUniversity of California Press185202 ItohS.Random fixed point theorems with an application to random differential equations in Banach spacesJournal of Mathematical Analysis and Applications19796722612735286870407.6006910.1016/0022-247X(79)90023-4 RhoadesB. E.Fixed point iteration using infinite matricesTransactions of the American Mathematical Society19741961611763485650285.4703810.1090/S0002-9947-1974-0348565-1 RhoadesB. E.Fixed point theorems and stability results for fixed point iteration proceduresIndian Journal of Pure and Applied Mathematics19902111910480100692.54027 BerindeV.On the convergence of the Ishikawa iteration in the class of quasi-contractive operatorsActa Mathematica Universitatis Comenianae200473111912620760501100.47054 ZhangS. S.Fixed Point Theory and Applications (in Chinese)1984ChongqingChongqing Publishing Press JoshiM. C.BoseR. K.Some Topics in Nonlinear Functional Analysis1985New DelhiWiley Eastern Limited0596.47038 BegI.AbbasM.Equivalence and stability of random fixed point iterative proceduresJournal of Applied Mathematics and Stochastic Analysis20062006119 BerindeV.On the stability of some fixed point proceduresBuletinul Stiintific al Universitatii Baia Mare, Seria B, Fascicola Matematica-Informatica200218171420142771031.47030 OlatinwoM. O.Some stability results for two hybrid fixed point iterative algorithms of Kirk-Ishikawa and Kirk-Mann typeJournal of Advanced Mathematical Studies2008115142498892 RhoadesB. E.Some theorems on weakly contractive mapsNonlinear Analysis2001472683269319723921042.4752110.1016/S0362-546X(01)00388-1 RhoadesB. E.Fixed point theorems and stability results for fixed point iteration procedures IIIndian Journal of Pure and Applied Mathematics1993241169170312511800794.54048 AlberY. I.Guerre-DelabriereS.GohbergI.LyubichY.Principle of weakly contractive maps in Hilbert spacesNew Results in Operator Theory and Its Applications1997SwitzerlandBirkhauser Verlag Basel722 S. S. Chang (1460_CR6) 2005; 23 B. E. Rhoades (1460_CR10) 2001; 47 S. Itoh (1460_CR5) 1979; 67 M. C. Joshi (1460_CR1) 1985 I. Beg (1460_CR7) 2006; 2006 V. Berinde (1460_CR8) 2004; 73 M. O. Olatinwo (1460_CR12) 2008; 1 B. E. Rhoades (1460_CR13) 1990; 21 S. S. Zhang (1460_CR2) 1984 O. Hans (1460_CR4) 1961 A. Špaček (1460_CR3) 1955; 5 Y. I. Alber (1460_CR15) 1997 B. E. Rhoades (1460_CR14) 1993; 24 V. Berinde (1460_CR11) 2002; 18 B. E. Rhoades (1460_CR9) 1974; 196 |
| References_xml | – reference: RhoadesB. E.Some theorems on weakly contractive mapsNonlinear Analysis2001472683269319723921042.4752110.1016/S0362-546X(01)00388-1 – reference: ZhangS. S.Fixed Point Theory and Applications (in Chinese)1984ChongqingChongqing Publishing Press – reference: BerindeV.On the convergence of the Ishikawa iteration in the class of quasi-contractive operatorsActa Mathematica Universitatis Comenianae200473111912620760501100.47054 – reference: BerindeV.On the stability of some fixed point proceduresBuletinul Stiintific al Universitatii Baia Mare, Seria B, Fascicola Matematica-Informatica200218171420142771031.47030 – reference: AlberY. I.Guerre-DelabriereS.GohbergI.LyubichY.Principle of weakly contractive maps in Hilbert spacesNew Results in Operator Theory and Its Applications1997SwitzerlandBirkhauser Verlag Basel722 – reference: HansO.Random operator equationsProceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability1961CaliforniaUniversity of California Press185202 – reference: ItohS.Random fixed point theorems with an application to random differential equations in Banach spacesJournal of Mathematical Analysis and Applications19796722612735286870407.6006910.1016/0022-247X(79)90023-4 – reference: JoshiM. C.BoseR. K.Some Topics in Nonlinear Functional Analysis1985New DelhiWiley Eastern Limited0596.47038 – reference: RhoadesB. E.Fixed point theorems and stability results for fixed point iteration procedures IIIndian Journal of Pure and Applied Mathematics1993241169170312511800794.54048 – reference: BegI.AbbasM.Equivalence and stability of random fixed point iterative proceduresJournal of Applied Mathematics and Stochastic Analysis20062006119 – reference: OlatinwoM. O.Some stability results for two hybrid fixed point iterative algorithms of Kirk-Ishikawa and Kirk-Mann typeJournal of Advanced Mathematical Studies2008115142498892 – reference: RhoadesB. E.Fixed point theorems and stability results for fixed point iteration proceduresIndian Journal of Pure and Applied Mathematics19902111910480100692.54027 – reference: ŠpačekA.Zufallige gleichungenCzechoslovak Mathematical Journal1955546246679854 – reference: RhoadesB. E.Fixed point iteration using infinite matricesTransactions of the American Mathematical Society19741961611763485650285.4703810.1090/S0002-9947-1974-0348565-1 – reference: ChangS. S.ChoY. J.KimJ. K.ZhouH. Y.Random Ishikawa iterative sequence with applicationsStochastic Analysis and Applications200523697721239441065.6008410.1081/SAP-200044432 – volume: 23 start-page: 69 year: 2005 ident: 1460_CR6 publication-title: Stochastic Analysis and Applications doi: 10.1081/SAP-200044432 – volume: 47 start-page: 2683 year: 2001 ident: 1460_CR10 publication-title: Nonlinear Analysis doi: 10.1016/S0362-546X(01)00388-1 – volume: 1 start-page: 5 issue: 1 year: 2008 ident: 1460_CR12 publication-title: Journal of Advanced Mathematical Studies – volume-title: Fixed Point Theory and Applications (in Chinese) year: 1984 ident: 1460_CR2 – volume: 18 start-page: 7 issue: 1 year: 2002 ident: 1460_CR11 publication-title: Buletinul Stiintific al Universitatii Baia Mare, Seria B, Fascicola Matematica-Informatica – volume-title: Some Topics in Nonlinear Functional Analysis year: 1985 ident: 1460_CR1 – volume: 67 start-page: 261 issue: 2 year: 1979 ident: 1460_CR5 publication-title: Journal of Mathematical Analysis and Applications doi: 10.1016/0022-247X(79)90023-4 – volume: 24 start-page: 691 issue: 11 year: 1993 ident: 1460_CR14 publication-title: Indian Journal of Pure and Applied Mathematics – volume: 21 start-page: 1 issue: 1 year: 1990 ident: 1460_CR13 publication-title: Indian Journal of Pure and Applied Mathematics – volume: 2006 start-page: 1 year: 2006 ident: 1460_CR7 publication-title: Journal of Applied Mathematics and Stochastic Analysis – volume: 73 start-page: 119 issue: 1 year: 2004 ident: 1460_CR8 publication-title: Acta Mathematica Universitatis Comenianae – volume: 5 start-page: 462 year: 1955 ident: 1460_CR3 publication-title: Czechoslovak Mathematical Journal doi: 10.21136/CMJ.1955.100162 – volume: 196 start-page: 161 year: 1974 ident: 1460_CR9 publication-title: Transactions of the American Mathematical Society doi: 10.1090/S0002-9947-1974-0348565-1 – start-page: 185 volume-title: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability year: 1961 ident: 1460_CR4 – start-page: 7 volume-title: New Results in Operator Theory and Its Applications year: 1997 ident: 1460_CR15 doi: 10.1007/978-3-0348-8910-0_2 |
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| Snippet | The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of... The purpose of this paper is to study the almost sure T -stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of... O177.91; The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some... |
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| SubjectTerms | Applications of Mathematics Banach space Classical Mechanics Convergence Fluid- and Aerodynamics Iterative algorithms Mathematical analysis Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operators Partial Differential Equations |
| Title | Almost sure T-stability and convergence for random iterative algorithms |
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