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1
Content available remote Degrees of the approximations by some special matrix means of conjugate Fourier series
Kranz Radosława, Rzepka Aleksandra, Sylwestrzak-Maślanka Ewa
Demonstratio Mathematica
|
2019
|
Vol. 52, nr 1
116--129
EN
In this paper we will present the pointwise and normwise estimations of the deviations considered by W. Łenski, B. Szal, [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] and S. Saini, U. Singh, [Boll. Unione Mat. Ital., 2016, 9, 495-504] under general assumptions on the class considered sequences defining the method of the summability. We show that the obtained estimations are the best possible for some subclasses of Lp by constructing the suitable type of functions.
2
Content available remote Approximation of functions and their conjugates in Lp and uniform metric by Euler means
Volosivets S. S., Tyuleneva A. A.
Demonstratio Mathematica
|
2018
|
Vol. 51, nr 1
141--150
EN
For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.
3
Content available remote On the approximation of integrable functions by some special matrix means of Fourier series
Kranz R., Rzepka A.
Demonstratio Mathematica
|
2017
|
Vol. 50, nr 1
351--359
EN
The results concerninig pointwise approximation and product of summability methods corresponding to the theorems of Xh. Z. Krasniqi [Poincare J. Anal. Appl., 2014, 1, 1-8] and W. Łenski and B. Szal [Math. Slovaca, 2016, 66(6), 1-12] are generalized. Some special cases are also formulated as corollaries.
4
Content available remote Approximation theorems for Szász-Mirakjan-Durrmeyer type operators
Herzog M.
Czasopismo Techniczne. Nauki Podstawowe
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2016
|
Y. 113, iss. 1-NP
43--53
EN
In this paper we study an integral modification of Szász-Mirakjan type operators. The modification will be called Szász-Mirakjan-Durrmeyer type operators as in many papers examining this type of operators. We give direct approximation theorems for these operators using the modulus of continuity and the modulus of smoothness for functions belonging to exponential weighted spaces.
PL
W artykule badamy całkową modyfikację operatorów typu Szásza-Mirakjana. Tę modyfikację będziemy nazywać operatorami typu Szász-Mirakjan-Durrmeyera, jak to się czyni w wielu pracach badających tego typu operatory. Podajemy twierdzenia aproksymacyjne wykorzystujące moduł ciągłości i moduł gładkości dla funkcji z wykładniczych przestrzeni wagowych.
5
Content available remote On the approximation of functions from Lp by some special matrix means of Fourier series
Kranz R., Rzepka A.
Fasciculi Mathematici
|
2015
|
Nr 55
81--90
EN
The results corresponding to some theorems of S. Lal [Appl. Math. and Comput. 209 (2009), 346-350] and the results of W. Lenski and B. Szal [Banach Center Publ., 95, (2011), 339-351] are shown. The better degrees of pointwise approximation than these in mentioned papers by another assumptions on summability methods for considered functions are obtained. From presented pointwise results the estimation on norm approximation are derived. Some special cases as corollaries are also formulated.
6
Content available remote On pointwise approximation of functions by some matrix means of conjugate Fourier series
Łenski W., Szal B.
Fasciculi Mathematici
|
2015
|
Nr 55
91--108
EN
The results corresponding to some theorems of S. Lal [Tamkang J. Math., 31(4)(2000), 279-288] and the results of the authors [Banach Center Publ. 92(2011), 237-247] are shown. The same degrees of pointwise approximation as in mentioned papers by significantly weaker assumptions on considered functions are obtained. From presented pointwise results the estimation on norm approximation with essentialy better degrees are derived. Some special cases as corollaries for iteration of the Norlund or the Riesz method with the Euler one are also formulated.
7
Content available remote The degree of approximation of functions from exponential weight spaces
Herzog M.
Czasopismo Techniczne. Nauki Podstawowe
|
2014
|
R. 111, z. 3-NP
21--29
EN
This paper presents a study of the approximation properties of modified Szász-Mirakyan operators for functions from exponential weight spaces. We present theorems giving the degree of approximation by these operators using a modulus of continuity.
PL
W artykule badamy aproksymacyjne własności zmodyfikowanych operatorów typu Szásza-Mirakyana dla funkcji z wykładniczych przestrzeni wagowych. Przedstawiamy twierdzenia podające rząd aproksymacji funkcji przez operatory tego typu, wykorzystując moduł ciągłości.
8
Content available remote On the approximation of conjugate functions from Lp by some special matrix means of conjugate Fourier series
Krantz R., Rzepka A.
Commentationes Mathematicae
|
2014
|
Vol 54, No. 2
191--202
EN
The results corresponding to some theorems of W. Łenski and B. Szal are shown. From the presented pointwise results the estimates on norm approximation are derived. Some special cases as corollaries are also formulated.
9
Content available remote Approximation of functions of two variables from exponential weight spaces
Herzog M.
Czasopismo Techniczne. Nauki Podstawowe
|
2012
|
R. 109, z. 1-NP
3--10
EN
In this paper we study approximative properties of modified Szasz-Mirakyan operators for functions of two variables from exponential weight spaces. We present theorems giving a degree of approximation by these operators for exponential bounded functions.
PL
W artykule przedstawiono aproksymacyjne własności zmodyfikowanych operatorów typu Szasza-Mirakyana dla funkcji dwóch zmiennych z wykładniczych przestrzeni wagowych. Wyprowadzono twierdzenia podające rząd aproksymacji funkcji ograniczonych wykładniczo przez operatory tego typu.
10
Content available remote On the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series
Krasniqi X. Z.
Commentationes Mathematicae
|
2012
|
Vol. 52, [Z] 2
207--215
EN
In this paper we generalize some results on the degree of approximation of continuous functions by matrix means related to partial sums of a Fourier series, obtained previously by some other authors (please consult references cited in this paper).
11
Content available remote Approximation of functions of two variables by modified Szasz-Mirakyan operators
Herzog M.
Commentationes Mathematicae
|
2012
|
Vol. 52, [Z] 1
3-9
EN
In this paper we study approximative properties of modified Szasz-Mirakyan operators for functions of two variables from polynomial weight spaces. We present some direct theorems giving a degree of approximation for these operators.
12
Content available remote Approximation by truncated Favard-Szász-Mirakjan operator of max-product kind
Bede B., Coroianu L., Gal S. G.
Demonstratio Mathematica
|
2011
|
Vol. 44, nr 1
105-122
EN
Starting from the study of the Shepard nonlinear operator of max-prod type made by Bede et al. in 2006 and 2008, in the book of Gal in 2008 (Open Problem 5.5.4, pp. 324-326) the Favard-Szász-Mirakjan max-prod type operator is introduced and the question of the approximation order by this operator is raised. In the paper of Bede and Gal in 2010, an answer is given by obtaining a pointwise upper estimate of the approximation error of the form (...), with C > 0 unexplicit absolute constant. The aim of this note is to obtain the order of uniform approximation (...) (with C = 6) by another operator, much simpler and called truncated Favard-Szász-Mirakjan operator of max-product kind and to prove by a counterexample that in some sense, in general this type of order of approximation with respect to (...) cannot be improved. In addition, for some subclasses of functions including, for example, the nondecreasing concave functions, the essentially better order (...) is obtained. Finally, some shape preserving properties are proved.
13
Content available remote On the strong approximation of functions by the Bernstein polynomials
Michałowicz A.
Fasciculi Mathematici
|
2007
|
Nr 37
27-33
EN
In this note we introduce the strong differences of function and its Bernstein polynomials and give approximation theorems for them. This note is motivated by results on the strong summability of trigonometric Fourier series given in [2] and by the paper [5].
14
Content available remote The rate of convergence by a new type of Meyer-König and Zeller operators
Gupta V., Abel U.
Fasciculi Mathematici
|
2004
|
Nr 34
15-23
EN
In the present paper we introduce a simple integral modification of Meyer-Konig and Zeller operators and study their rate of convergence, for functions of bounded variation.
15
Content available remote Some remarks of Borel type means of trigonometric Fourier series
Tomczak K.
Fasciculi Mathematici
|
2004
|
Nr 34
121-128
EN
In this note we consider certain means Bi (f) of Borel type of trigonometric Fourier series of function f belonging to the Hölder space formula We give theorem on the degree of approximation of .
16
Content available remote Certain modification of Szasz-Mirakyan operators
Walczak Z.
Fasciculi Mathematici
|
2004
|
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.
17
Content available remote Approximation properties of certain modified Szasz-Mirakyan operators of functions of two variables
Walczak Z.
Fasciculi Mathematici
|
2004
|
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.
18
Content available remote Approximation by modified Favard operators
Rempulska L., Tomczak K.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2004
|
Vol. 44, nr 2
205-215
EN
We introduce certain modification of the Favard and Favard-Durrmeyer operators and we give some approximation properties for them. The similar results for the modified Bernstein polynomials are given in [5].
19
Content available remote Approximation of functions from exponential weight spaces by operators of Szász-Mirakyan type
Herzog M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2003
|
[Z] 43(1)
77-94
EN
In this paper we will study properties of Szasz-Mirakyan type operators defined by modified Bessel function. We shall present Voronovskaya type theorem and theorems giving a degree of approximation by these operators for exponential bounded function.
20
Content available remote Approximation of functions of one and two variables by some operators
Rempulska L., Skorupka M.
Fasciculi Mathematici
|
2002
|
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.
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