On the Approximation of Zeros of Non-Self Monotone Operators. (2nd June 2016)

• Record Type: Journal Article
• Authors: Colao, Vittorio; Marino, Giuseppe; Muglia, Luigi
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 6(2016)
• Page Start: 667
• Page End: 679
• Publication Date: 2016-06-02
• Subjects: Approximation -- inverse strongly monotone operators -- non-self mappings -- strict pseudo contraction -- zeros of operators; 47H05 -- 47H10 -- 65J05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1177727
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study the approximation of common zeros of non-self inverse strongly monotone operators defined on a closed convex subset C of a Hilbert space H . For a non-self family of operators, we introduce an iterative algorithm without relying on projections. Approximation of common fixed points for finite families of non-self strict pseudo-contractions in the sense of Browder-Petryshyn is also obtained. The novelty of our algorithm is that the coefficients are not given a priori and no assumptions are made on them, but they are constructed step by step in a natural way.