Exponential inequalities for Mann's stochastic algorithm. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Allouti, Chahira; Barache, Bahia; Dahmani, Abdelnasser
• Is Part Of: Sequential analysis. Volume 39:Issue 1(2020)
• Page Start: 32
• Page End: 51
• Publication Date: 2020-01-02
• Subjects: Almost complete convergence -- fixed point -- Mann iteration -- negative association -- quasi-associated random errors -- rate of convergence; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2020.1726681
• Languages: English
• ISSNs: 0747-4946

Abstract

Abstract: In this article, we investigate the problem of approximating the fixed point for some function using a Mann iterative process with random errors. After establishing some exponential inequalities, we prove the complete convergence of Mann's algorithm toward the fixed point and deduce a confidence interval for this one. In addition, we establish the convergence rate of Mann's algorithm. Several numerical examples are sketched to illustrate the performance of the proposed algorithm.