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EN
In this paperwe will prove the Korovkin type theorem for modified Szász-Mirakyan operators via Astatistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem.
EN
In present article, we discuss voronowskaya type theorem, weighted approximation in terms of weighted modulus of continuity for Szász type operators using Sheffer polynomials. Lastly, we investigate statistical approximation for these sequences.
EN
In this paper we introduce some linear positive operators of the Baskakov-Durrmeyer type in the space of uniformly continuous and bounded functions of several variables. The theorem on the degree of the convergence is established. Moreover, we give the Voronovskaya type formula for these operators.
PL
W artykule rozważa się operatory typu Baskakowa-Durrmeyera w przestrzeni ograniczonych i jednostajnie ciągłych funkcji wielu zmiennych. Formułuje się i dowodzi twierdzenia dotyczące rzędu zbieżności, jak również twierdzenie typu Woronowskiej dla tych operatorów.
4
Content available remote On the rates of convergence of certain bivariate linear positive operators
EN
In this paper, we present a sequence of linear positive bivariate operators and investigate the approximation properties of them. Next we study the rates of converge of this approximation by means modulus of continuity and functions from Lipschitz class. After we give a Voronovskaya type theorem for n Morever, we give an r th order generalization of these operators. Finally, we investigate approximation properties of this generalization and observe the rates of convergence for them.
5
Content available remote Direct estimate for some operators of Durrmeyer type in exponential weighted space
EN
In the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.
6
Content available remote On the Baskakov-Durrmeyer type operators
EN
In this paper we will study some approximate properties of Baskakov-Durrmeyer type operators Mα,an. We determine the rate of convergence and prove the Voronovskaya type theorem for those operators.
7
Content available remote On some class of exponential type operators
EN
Starting from a differential equation [formula] for the kernel of an operator [formula] with the normalization condition [formula] we provesome properties which are similar to properties proved by Ismailand May for the exponential operators. In particular, we show thatall these operators are approximation operators. Moreover, amethod of determining [formula] for a given function isintroduced.
8
Content available remote On certain modified Szasz-Mirakyan operators for functions of two variables
EN
We introduce certain modified Szasz-Mirakyan operators in polynomial weighted spaces of functions of two variables and we study approximation properties of these operators. The similar theorems for function of one variable are given in [2].
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