Convergence of Iterated Boolean-type Sums and Their Iterates. (27th July 2018)

• Record Type: Journal Article
• Authors: Campiti, Michele
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 10(2018)
• Page Start: 1054
• Page End: 1063
• Publication Date: 2018-07-27
• Subjects: Bernstein operators -- Bernstein–Durrmeyer operators -- iterated Boolean sums -- representation of semigroups and resolvent operators; 41A10 -- 41A36 -- 47D06; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1467446
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The convergence of iterated Boolean sums for different sequences of operators has been studied keeping fixed the number M of iterations or recently letting for a fixed operator. Here we consider some convergence properties of iterated Boolean-type sums of the classical Bernstein and Bernstein–Durrmeyer operators in the case where both the operators and their order of iterations are not fixed. In the case of Bernstein–Durrmeyer operators, we obtain a general solution of this problem. We can also state some alternative expressions of the semigroups and resolvent operators associated with the Voronovskaja's formula for these sequences of operators.