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Vectorial generalized g–fractional direct and iterated approximations by linear operators

Anastassiou George A.

Fasciculi Mathematici

2020

nr 64

17--42

In this work we consider quantitatively with rates the convergence of sequences of linear operators applied on Banach space valued functions. The results are pointwise estimates with rates. To prove our main results we use an elegant and natural boundedness property of our linear operators by their companion positive linear operators. Our inequalities are generalized g-direct and iterated fractional involving the right and left vector Caputo type generalized g-direct and iterated fractional derivatives, built in vector moduli of continuity. We treat wide and general classes of Banach space valued functions. We give applications to vectorial Bernstein operators.

An investigation of the approximation of functions of two variables by the Poisson integral for Hermite expansions

Krech G.

Czasopismo Techniczne. Nauki Podstawowe

2014

R. 111, z. 3-NP

31--38

This paper presents a study of the approximation properties of the Poisson integral for Hermite expansions in the space Lp. The rate of convergence of functions of two variables by these integrals is established.

Artykuł poświęcony jest własnościom aproksymacyjnym całek Poissona związanych z wielomianami Hermite’a. Udowodniono twierdzenie o rzędzie zbieżności funkcji dwóch zmiennych w przestrzeni Lp tymi operatorami.

Statistical approximation for periodic functions

Duman O.

Demonstratio Mathematica

2003

Vol. 36, nr 4

873--878

In this paper we study a Korovkin type approximation theorem for positive linear operators on the space of all 2π-periodic and continuous functions on the whole real axis via A-statistical convergence.