Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (6): 805-810.doi: https://doi.org/10.1007/s10483-011-1460-6

• Articles • 上一篇    

Almost sure T-stability and convergence for random iterative algorithms

张石生 王雄瑞 刘敏 朱浸华   

  • 收稿日期:2010-11-21 修回日期:2011-04-08 出版日期:2011-06-01 发布日期:2011-06-01

Almost sure T-stability and convergence for random iterative algorithms

 ZHANG Shi-Sheng, WANG Xiong-Rui, LIU Min, ZHU Jin-Hua   

  • Received:2010-11-21 Revised:2011-04-08 Online:2011-06-01 Published:2011-06-01

摘要: 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.

关键词: almost sure T-stability, separable Banach space, Bochner integrability, Ishikawa-type random iterative scheme, Mann-type random iterative scheme

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 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.

Key words: almost sure T-stability, separable Banach space, Bochner integrability, Ishikawa-type random iterative scheme, Mann-type random iterative scheme

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