Application of Popoviciu’s high convexity to the study of some sequences properties

2 years ago

(proceedings), Approximation Theory, Linear and positive approximation operators, not-at-ICTP, paper

Abstract

Starting by the notion of convex funcitons of $n$ -order introduced by Tiberiu Popoviciu, we aim to record those theorems obtained in time by several mathematicians, which show how the behaviour of a function $f$ is mirrored by sequences of linear and positive operators. From the perspective openend by T. Popoviciu, this survey paper presents the monotonicity properties of the well-known operators of Bernstein, Bleimann Butzer and Hahn, Meyer Koning and Zeller, Szasz Favard-Mirakyan and Baskakov. This way we take the opportunity to emphasize the importance of the powerful school founded by Popoviciu in Cluj.

Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

n-convexity; n-th divided difference; Meyer-Konig and Zeller operator; Favard-Szasz-Mirakyan operator; Baskakov operator

Paper coordinates

O. Agratini, Application of Popoviciu’s high convexity to the study of some sequences properties, Seminaire de la Theorie de la Meilleure Approximation, Convexite et Optimisation Cluj-Napoca, 26 octobre – 29 octobre, 2000, pp. 1-15.

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