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1
Content available remote Voronovskaya-Type Theorems for Derivatives of the Bernstein-Chlodovsky Polynomials and the Szasz-Mirakyan Operator
Butzer P.L., Karsli H.
Commentationes Mathematicae
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2009
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Vol. 49, [Z] 1
33-58
EN
This paper is devoted to a study of a Voronovskaya-type theorem for the derivative of the Bernstein-Chlodovsky polynomials and to a comparison of its approximation eectiveness with the corresponding theorem for the much better-known Szasz-Mirakyan operator. Since the Chlodovsky polynomials contain a factor bn tending to innity having a certain degree of freedom, these polynomials turn out to be generally more ecient in approximating the derivative of the associated function than does the Szasz operator. Moreover, whereas Chlodovsky polynomials apply to functions which are even of order O(exp(x^p)) for any p ≥ 1; the Szasz-Mirakyan operator does so only for p = 1; it diverges for p > 1. The proofs employ but rene practical methods used by Jerzy Albrycht and Jerzy Radecki ( in papers which are almost never cited ) as well as by further mathematicians from the great Poznań school.
2
Content available remote Rate of approximation for integrated Szasz-Mirakyan operators
Dubey D., Jain V.
Demonstratio Mathematica
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2008
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Vol. 41, nr 4
879-886
EN
Recently Jain et al. [3] proposed an integral modification of Szasz-Mirakyan operators Sn,alpha(f,x),alpha > O and studied some direct approximation theorems in simultaneous approximation. The present paper deals with the rate of approximation of such operators, for functions which have derivatives of bounded variation.
3
Content available remote Certain modification of Szasz-Mirakyan operators
Walczak Z.
Fasciculi Mathematici
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2004
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Nr 34
141-147
EN
We consider certain modified Szasz-Mirakyan operators An (f; r) in space C0 of uniformly continuous functions. We study approximation properties of these operators.
4
Content available remote Approximation properties of certain modified Szasz-Mirakyan operators of functions of two variables
Walczak Z.
Fasciculi Mathematici
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2004
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Nr 34
129-140
EN
We introduce certain modified Szasz-Mirakyan operators in polynomial and exponential weighted spaces of functions of two variables and we study the degree of approximation of functions by these operators.
5
Content available remote Direct and converse theorems for integral-type operators
Finta Z.
Demonstratio Mathematica
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2003
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Vol. 36, nr 1
137--147
EN
We establish direct and converse results for integral-type operators defined with the aid of Szasz-Mirakjan operator and Baskakov operator, respectively. Moreover, some applications will be given.
6
Content available remote Approximation of functions of one and two variables by some operators
Rempulska L., Skorupka M.
Fasciculi Mathematici
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2002
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Nr 33
57-87
EN
We consider some operates of Szasz-Mirakyan type in exponential weighted spaces of functions of one and two variables. We give theorems on the degree of approximation of functions by these operators and the Voronovskaya type theorems.
7
Content available remote Approximation of functions of two variables by modified Szasz-Mirakyan operators
Walczak Z.
Fasciculi Mathematici
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2001
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Nr 31
117-128
EN
We consider certain modified Szasz-Mirakyan operators in the exponential weighted spaces of continuous functions of two variables. We prove theorems on the degree of approximation, the Voronovskaya type theorem and we study some differential properties of these operators. The similar results for functions of one variable were given in [1] and [2].
8
Content available remote On certain modified Szasz-Mirakyan operators for functions of two variables
Walczak Z.
Demonstratio Mathematica
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2000
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Vol. 33, nr 1
91-100
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].
9
Content available remote Approximation theorems for some operators in weghted spaces of functions of two variables
Gurdek M., Kurczyńska J., Walczak Z.
Fasciculi Mathematici
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1999
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Nr 30
23-35
EN
We study approximation properties of the Baskakov-Szasz-Mirakyan operators in some weighted spaces of functions of two variables. For these operators we give two theorems on the degree of approximation and the Voronovskaya type theorem. The Szasz-Mirakyan and Baskakov operators in the polynomial and exponential weighted spaces of functions of one variable were examined in [1]-[4]. Approximation theorems and the Voronovskaya type theorem for some operators ofthe Szasz-Mirakyan type were given in [5]-[7].
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