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


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.


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


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

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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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