• Corpus ID: 222141751

Semi-discrete Gruss-Voronovskaya-type and Gruss-type estimates for Bernstein-Kantorovich polynomials

@article{Gal2020SemidiscreteGA,
  title={Semi-discrete Gruss-Voronovskaya-type and Gruss-type estimates for Bernstein-Kantorovich polynomials},
  author={Sorin G. Gal},
  journal={arXiv: Classical Analysis and ODEs},
  year={2020}
}
  • S. Gal
  • Published 25 September 2020
  • Mathematics
  • arXiv: Classical Analysis and ODEs
The aim of this note is to prove a semi-discrete Gruss-Voronovskaya-type estimate for Bernstein-Kantorovich polynomials. Also, as a consequence, a perturbed Gruss-type estimate is obtained. 

References

SHOWING 1-10 OF 16 REFERENCES
Semi-discrete Quantitative Voronovskaya-Type Theorems for Positive Linear Operators
Because all the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange–Hermite
The Bernstein Voronovskaja-type theorem for positive linear approximation operators
We prove that the classical Bernstein Voronovskaja-type theorem remains valid in general for all sequences of positive linear approximation operators.
Classical Kantorovich Operators Revisited
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 continuity which
Čebyšev-Grüss-type inequalities revisited
We generalize and improve several inequalities of the Čebyšev-Grüss-type using least concave majorants of the moduli of continuity of the functions involved. Our focus is on normalized positive
Gr\"uss and Gr\"uss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables
The first aim of this paper is to prove a Gr\"uss-Voronovskaya estimate for Bernstein and for a class of Bernstein-Durrmeyer polynomials on $[0, 1]$. Then, Gr\"uss and Gr\"uss-Voronovskaya estimates
Grüss-type and Ostrowski-type inequalities in approximation theory
We discuss the Grüss inequalities on spaces of continuous functions defined on a compact metric space. Using the least concave majorant of the modulus of continuity, we obtain the Grüss inequality
On the degree of approximation in Voronovskaya's theorem. Stud. Univ
  • Babes-Bolyai" ser. math
  • 2007
On the degree of approximation in Voronovskaya’s theorem
  • Stud. Univ. ”Babes-Bolyai” ser. math. LII (3),
  • 2007
The asymptotic value of the approximation of multiply differentiable functions by positive linear operators
  • Dokl. Akad. Nauk SSSR 146,
  • 1962
: Complément à l ’ article de E . Voronovskaya ” Détermination de la forme asymptotique de l ’ approximation des fonctions par les polynômes de M . Bernstein ”
  • C . R . Acad . Sci . URSS
  • 1932
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