scholarly journals On approximation properties of Baskakov-Schurer-Szász operators preserving exponential functions

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5433-5440 ◽  
Author(s):  
Övgü Yılmaz ◽  
Murat Bodur ◽  
Ali Aral
Keyword(s):  
Uniform Convergence ◽  
Generating Function ◽  
General Class ◽  
Quantitative Estimate ◽  
Moment Generating Function ◽  
Convergence Result ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Szász Operators

The goal of this paper is to construct a general class of operators which has known Baskakov-Schurer-Sz?sz that preserving constant and e2ax, a > 0 functions. Also, we demonstrate the fact that for these operators, moments can be obtained using the concept of moment generating function. Furthermore, we investigate a uniform convergence result and a quantitative estimate in consideration of given operator, as well. Finally, we discuss the convergence of corresponding sequences in exponential weighted spaces and make a comparison about which one approximates better between classical Baskakov-Schurer-Sz?sz operators and the recent sequence, too.

scholarly journals Approximation by modified Păltănea operators

2020 ◽  
Vol 107 (121) ◽  
pp. 157-164
Author(s):  
Vijay Gupta ◽  
P.N. Agrawal
Keyword(s):  
Generating Function ◽  
Type Theorem ◽  
Moment Generating Function ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaya Type Theorem

We discuss some approximation properties of hybrid genuine operators. We find central moments using the concept of moment generating function. A quantitative Voronovskaya and Gruss-Voronovskaya type theorem are proven. Also, we obtain the degree of approximation of the considered operators by means of the second order Ditzian-Totik modulus of smoothness.

scholarly journals Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Modulus Of Continuity ◽  
Maximal Functions ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Type Result ◽  
Quantum Calculus ◽  
Szász Operators

Abstract The main purpose of this paper is to introduce a generalized class of Dunkl type Szász operators via post quantum calculus on the interval $[ \frac{1}{2},\infty )$ [ 1 2 , ∞ ) . This type of modification allows a better estimation of the error on $[ \frac{1}{2},\infty ) $ [ 1 2 , ∞ ) rather than $[ 0,\infty )$ [ 0 , ∞ ) . We establish Korovkin type result in weighted spaces and also study approximation properties with the help of modulus of continuity of order one, Lipschitz type maximal functions, and Peetre’s K-functional. Furthermore, we estimate the degrees of approximations of the operators by modulus of continuity of order two.

scholarly journals On a special class of modified integral operators preserving some exponential functions

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Gümrah Uysal
Keyword(s):  
Uniform Convergence ◽  
General Class ◽  
Special Class ◽  
Integral Operators ◽  
Quantitative Result ◽  
Kernel Functions ◽  
Exponential Functions ◽  
Type Estimate

<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id="M1">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id="M2">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} _{0}^{+} $\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

scholarly journals Semi-Exponential Operators

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 637
Author(s):  
Monika Herzog
Keyword(s):  
Exponential Type ◽  
Probabilistic Approach ◽  
Weighted Spaces ◽  
Approximation Properties

In this paper we study approximation properties of exponential-type operators for functions from exponential weighted spaces. We focus on some modifications of these operators and we derive a new example of such operators. A probabilistic approach for these modifications is also demonstrated.

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

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