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Remarks on a Bernstein-type operator of Aldaz, Kounchev and Render
Ana-Maria Acu, Heiner Gonska, Margareta Heilmann
The Bernstein-type operator of Aldaz, Kounchev and Render (2009) is discussed. New direct results in terms of the classical second order modulus as well as in a modification follow…
Elementary hypergeometric functions, Heun functions, and moments of MKZ operators
Ana Maria Acu, Ioan Rasa
We consider some hypergeometric functions and prove that they are elementary functions. Consequently, the second order moments of Meyer-Konig and Zeller type operators are elementa…
Classical Kantorovich operators revisited
Ana Maria Acu, Heiner Gonska
The main object of this paper is to improve some of the known estimates for classical Kantorovich operators. A quantitative Voronovskaya-type result in terms of second moduli of co…
Generalized Alomari functionals
Ana Maria Acu, Heiner Gonska
We consider a generalized form of certain integral inequalities given by Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson, Newton-Simpson rules are obtained as…
Weighted Ostrowski-Grüss type inequalities
Ana Maria Acu, Heiner Gonska
Several inequalities of Ostrowski-Gruss-type availabe in the literature are generalized by considering the weighted case of them. Involving the least concave majorant of the modul…
On Bullen's and related inequalities
Ana Maria Acu, Heiner Gonska
The estimate in Bullen's inequality will be extended for continuous functions using the second order modulus of smoothness. A different form of this inequality will be given in ter…