36 citations · 72 across the 12 of their papers we have counts for
15 papers
Overiteration of -variate tensor product Bernstein operators: a quantitative result
Ana-Maria Acu, Heiner Gonska
Extending an earlier estimate for the degree of approximation of overiterated univariate Bernstein operators towards the same operator of degree one, it is shown that an analogous…
Brass-Stancu-Kantorovich Operators on a Hypercube
Gülen Başcanbaz-Tunca, Heiner Gonska
We deal with multivariate Brass-Stancu-Kantorovich operators depending on a non-negative integer parameter and defined on the space of all Lebesgue integrable functions on a unit h…
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…
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…
Perturbed Bernstein-type operators
Ana Maria Acu, Heiner Gonska
The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct…
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…
Composite Bernstein Cubature
Ana-Maria Acu, Heiner Gonska
We consider a sequence of composite bivariate Bernstein operators and the cubature formula associated with them. The upper bounds for the remainder term of the cubature formula are…
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…
Lagrange-type operators associated with
Heiner Gonska, Ioan Raşa, Elena-Dorina Stănilă
We consider a class of positive linear operators which, among others, constitute a link between the classical Bernstein operators and the genuine Bernstein-Durrmeyer mappings. The…
Beta operators with Jacobi weights
Heiner Gonska, Ioan Raşa, Elena Dorina Stănilă
We discuss Beta operators with Jacobi weights on for , thus including the discussion of three limiting cases. Emphasis is on the moments and their asymptotic be…
Power series of the operators
Heiner Gonska, Ioan Raşa, Elena Dorina Stănilă
We study power series of members of a class of positive linear operators reproducing linear function and constituting a link between genuine Bernstein-Durrmeyer and classical Berns…
Chebyshev-Grüss-type inequalities via discrete oscillations
Heiner Gonska, Ioan Raşa, Maria-Daniela Rusu
The classical form of Grüss' inequality, first published by G. Grüss in 1935, gives an estimate of the difference between the integral of the product and the product of the integra…
Grüss and Grüss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables
Sorin Gal, Heiner Gonska
The first aim of this paper is to prove a Grüss-Voronovskaya estimate for Bernstein and for a class of Bernstein-Durrmeyer polynomials on . Then, Grüss and Grüss-Voronovska…
On the composition and decomposition of positive linear operators III: A non-trivial decomposition of the Bernstein operator
Heiner Gonska, Margareta Heilmann, Alexandru Lupaş +1
The central problem in this technical report is the question if the classical Bernstein operator can be decomposed into nontrivial building blocks where one of the factors is the g…