Exponential inequalities for Mann's iterative scheme with functional random errors. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Barache, Bahia; Arab, Idir; Dahmani, Abdelnasser
• Is Part Of: Sequential analysis. Volume 37:Issue 1(2018)
• Page Start: 18
• Page End: 30
• Publication Date: 2018-01-02
• Subjects: Almost complete -- convergence -- confidence domain -- fixed point iteration -- Mann's algorithm -- rate of convergence -- Stochastic methods; 76M35 -- 60H35; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2018.1427964
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: In this article, we deal with an iteration method for approximating a fixed point of a contraction mapping using Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of an exponential inequality and then we specify the induced rate of convergence. We finally build a confidence domain for the fixed point. Moreover, some numerical examples are considered.