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1
Content available remote Convergence of generalized sampling series in weighted spaces
Acar Tuncer, Alagöz Osman, Aral Ali, Costarelli Danilo, Turgay Metin, Vinti Gianluca
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
153--162
EN
The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.
2
Content available remote A note on the convergence of Phillips operators by the sequence of functions via q-calculus
Kiliçman Adem, Ayman-Mursaleen Mohammad, Nasiruzzaman Md.
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
615--633
EN
The basic aim of this study is to include nonnegative real parameters to allow for approximation findings of the Stancu variant of Phillips operators. We concentrate on the uniform modulus of smoothness in a simple manner before moving on to the approximation in weighted Korovkin’s space. Our study’s goals and outcomes are to fully develop the uniformly approximated findings of Phillips operators. We determine the order of convergence in terms of Lipschitz maximal function and Peetre’s K-functional. In addition, the Voronovskaja-type theorem is also proved.
3
Deferred weighted A-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems
Srivastava H. M., Jena B. B., Paikray S. K., Misra U. K.
Journal of Applied Analysis
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2018
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Vol. 24, nr 1
1--16
EN
Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and A-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911-6918]. In our present investigation, we introduce a certain deferred weighted A-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and t2 defined on a Banach space C[0,1] for a sequence of (presumably new) positive linear operators based upon (p,q)-Lagrange polynomials. Furthermore, we investigate the deferred weighted A-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.
4
Content available remote Rate of convergence of Szász-beta operators based on q-integers
Gupta P., Agrawal P. N.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
130--143
EN
The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.
5
Content available remote Multivariate and abstract approximation theory for Banach space valued functions
Anastassiou G. A.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
208--222
EN
Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators for which we study their approximation properties. We derive pointwise and uniform estimates, which imply the approximation of these operators to the unit assuming Fréchet differentiability of functions, and then we continue with basic approximations. At the end we study the special case where the approximated function fulfills a convexity condition resulting into sharp estimates. We give applications to Bernstein operators.
6
Content available remote Approximation properties of Ibragimov-Gadjiev-Durrmeyer operators on Lp (R+)
Ulusoy G., Aral A.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
156--174
EN
We deal with the approximation properties of a new class of positive linear Durrmeyer type operators which offer a reconstruction of integral type operators including well known Durrmeyer operators. This reconstruction allows us to investigate approximation properties of the Durrmeyer operators at the same time. It is first shown that these operators are a positive approximation process in Lp (R+). While we are showing this property of the operators we consider the Ditzian-Totik modulus of smoothness and corresponding K-functional. Then, weighted norm convergence, whose proof is based on Korovkin type theorem on Lp (R+), is given. At the end of the paper we show several examples of classical sequences that can be obtained from the Ibragimov-Gadjiev-Durrmeyer operators.
7
Content available remote Approximation by q-analogue of modified Jakimovski-Leviatan-Stancu type operators
Mursaleen M., Nasiruzzaman M., Wafi A.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
175--189
EN
In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modied operators introduced by Atakut with the help of the q-Appell polynomials. We obtain some approximation results via the well-known Korovkin’s theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover, we study the rate of convergence in terms of modulus of continuity of these operators in a weighted space.
8
Content available remote Approximation theorems for Szász-Mirakjan-Durrmeyer type operators
Herzog M.
Czasopismo Techniczne. Nauki Podstawowe
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2016
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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.
9
On the order of weighted approximation of unbounded functions by some generalizations of Gadjiev-Ibragimov operators
Ghorbanalizadeh A. M
Journal of Applied Analysis
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2014
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Vol. 20, nr 1
87--92
EN
The generalization of Gadjiev–Ibragimov operators by means of Kantorovich and Kirov–Popova is considered and the order of weighted approximation of unbounded functions are obtained.
10
Content available remote The degree of approximation of functions from exponential weight spaces
Herzog M.
Czasopismo Techniczne. Nauki Podstawowe
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2014
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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.
11
Content available remote Approximation of functions of two variables from exponential weight spaces
Herzog M.
Czasopismo Techniczne. Nauki Podstawowe
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2012
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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.
12
Content available remote On certain Kantorovich type operators
Erençin A., Taşdelen F.
Fasciculi Mathematici
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2009
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Nr 41
65-71
EN
In the present paper, we introduce a generalization of the Kantorovich type operators K*n(f;x) defined in [1]. We give approximation properties of these operators with the help of Bohman-Korovkin Theorem. We also compute rate of convergence by means of modulus of continuity, the elements of local Lipschitz class and Peetre's K-functional.
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