Gr\"uss and Gr\"uss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables

By Sorin G. Gal, Heiner Gonska. 2014

66 citations recorded by the source corpus.

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 for their corresponding operators of complex variable on compact disks are obtained. Finally, the results are extended to Bernstein-Faber polynomials attached to compact sets in the complex plane.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c052d224dff3575adf66beb03765d106464842d1

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In Applied Mathematics

1. Tuncer Acar
2. Gülsüm Ulusoy

In Numerical Analysis

1. Gülsüm Ulusoy
2. Tuncer Acar
3. Syed Abdul Mohiuddine

In Statistics and Probability

1. Gülsüm Ulusoy
2. Tuncer Acar
3. Syed Abdul Mohiuddine

Citations in the corpus

• Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators (2016, methodology): “In [10], Gal and Gonska obtained a Voronovskaya-type theoremwith the aid of the Grüss inequality for Bernstein operators for the first time and called it Grüss–Voronovskaya-type theorem.”
• q‐Voronovskaya type theorems for q‐Baskakov operators (2016, methodology): “In [19], Gal and Gonska obtained a Voronovskaya type theorem with the aid of Grüss inequality for Bernstein operators for the first time and called Grüss-Voronovskaya type theorem.”