On a Class of Bernstein-Type Rational Functions. (11th March 2020)

• Record Type: Journal Article
• Authors: Agratini, Octavian
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 4(2020)
• Page Start: 483
• Page End: 494
• Publication Date: 2020-03-11
• Subjects: Abdulofizov generalization -- Balázs-Szabados operator -- Korovkin theorem -- linear positive operator -- modulus of smoothness; Primary: 41A25 -- Secondary: 47A63; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1664566
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This note aims to highlight a general class of discrete linear and positive operators, focusing on some of their approximation properties. The construction includes a sequence of positive numbers ( λ n ), strictly decreasing. Imposing additional conditions on it, we set the convergence of the operators towards the identity operator and establish upper bounds for the error of approximation. A probabilistic approach is given. Also, in certain weighted spaces the study of its approximation properties is developed.