Best constants for tensor products of Bernstein, Szász and Baskakov operators

Generalized Baskakov-Szász type operators

Keywords: Baskakov-Szász operators Modulus of continuity Asymptotic formula Simultaneous approximation Statistical convergence Bounded variation a b s t r a c t In the present paper, we introduce generalized Baskakov-Szász type operators and study some approximation properties of these operators e.g., rate of convergence in ordinary and simultaneous approximation, statistical convergence and th...

Best constants in preservation of global smoothness for Szász – Mirakyan operators ✩

We obtain the best possible constants in preservation inequalities concerning the usual first modulus of continuity for the classical Szász–Mirakyan operator. The probabilistic representation of this operator in terms of the standard Poisson process is used. © 2007 Elsevier Inc. All rights reserved.

Best Constants for Certain Multilinear Integral Operators

Hilbert’s proof, apart from the determination of the best possible constant π csc(π/p), was published by Weyl [7]. The calculation of the constant, and the integral analogue of Hilbert’s double series theorem (for p = 2) are due to Schur [6]. The generalizations to other p′s of both the discrete and integral versions of this result were discovered later on by Hardy and Riesz and published by Ha...

On some constants in approximation by Bernstein operators

We estimate the constants sup x∈(0,1) sup f∈C[0,1]\Π1 |Bn(f,x)−f(x)| ω2 f, x(1−x) n and inf x∈(0,1) sup f∈C[0,1]\Π1 |Bn(f,x)−f(x)| ω2 f, x(1−x) n , where Bn is the Bernstein operator of degree n and ω2 is the second order modulus of continuity. 2000 Mathematical Subject Classification: 41A36, 41A10, 41A25,

Spectra of Tensor Products of Operators