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Approximation problems in modular spaces of double sequences.

Aleksander Waszak (1990)

Publicacions Matemàtiques

Let X denote the space of all real, bounded double sequences, and let Φ, φ, Γ be φ-functions. Moreover, let Ψ be an increasing, continuous function for u ≥ 0 such that Ψ(0) = 0.In this paper we consider some spaces of double sequences provided with two-modular structure given by generalized variations and the translation operator (...).

Approximation properties for modified ( p , q ) -Bernstein-Durrmeyer operators

Mohammad Mursaleen, Ahmed A. H. Alabied (2018)

Mathematica Bohemica

We introduce modified ( p , q ) -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators D n , p , q * and compute the rate of convergence for the function f belonging to the class Lip M ( γ ) .

Approximation properties of bivariate complex q -Bernstein polynomials in the case q > 1

Nazim I. Mahmudov (2012)

Czechoslovak Mathematical Journal

In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q -Bernstein polynomials for a function analytic in the polydisc D R 1 × D R 2 = { z C : | z | < R 1 } × { z C : | z | < R 1 } for arbitrary fixed q > 1 . We give quantitative Voronovskaja type estimates for the bivariate q -Bernstein polynomials for q > 1 . In the univariate case the similar results were obtained by S. Ostrovska: q -Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution...

Approximation properties of q-Baskakov operators

Zoltán Finta, Vijay Gupta (2010)

Open Mathematics

We establish direct estimates for the q-Baskakov operator introduced by Aral and Gupta in [2], using the second order Ditzian-Totik modulus of smoothness. Furthermore, we define and study the limit q-Baskakov operator.

Approximation results for nonlinear integral operators in modular spaces and applications

Ilaria Mantellini, Gianluca Vinti (2003)

Annales Polonici Mathematici

We obtain modular convergence theorems in modular spaces for nets of operators of the form ( T w f ) ( s ) = H K w ( s - h w ( t ) , f ( h w ( t ) ) ) d μ H ( t ) , w > 0, s ∈ G, where G and H are topological groups and h w w > 0 is a family of homeomorphisms h w : H h w ( H ) G . Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

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