Beta operators with Jacobi weights

Gonska, Heiner; Raşa, Ioan; Stănilă, Elena Dorina

doi:10.48550/arxiv.1402.3485

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2015

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“…În ecuat ¸ia de mai sus, B a,b r este operatorul Euler-Jacobi-Beta definit în [9] şi B n , B m sunt operatorii Bernstein de ordin n şi m. A doua clasȃ de operatori liniari şi pozitivi pe care îi considerȃm sunt BEJ de tipul II. Definit ¸ia este datȃ în continuare.…”

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Inegalităţi de tip Chebyshev-Grüss pentru operatorii Bernstein-Euler-Jacobi

Gonska¹,

Rusu²,

Stănilă³

2015

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The classical form of Grüss' inequality was first published by G. Grüss and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to consider some Chebyshev-Grüss-type inequalities and apply them to the Bernstein-Euler-Jacobi (BEJ) operators of first and second kind. The first and second moments of the operators will be of great interest.

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