Some approximation properties of a Durrmeyer variant ofq-Bernstein-Schurer operators

2016 ◽  
Vol 39 (18) ◽  
pp. 5636-5650 ◽  
Author(s):  
Ana-Maria Acu ◽  
Carmen Violeta Muraru ◽  
Daniel Florin Sofonea ◽  
Voichiţa Adriana Radu
Keyword(s):  
Approximation Properties ◽  
Durrmeyer Variant

scholarly journals Better approximation by a Durrmeyer variant of $ \alpha- $Baskakov operators

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Purshottam Narain Agrawal ◽  
Jitendra Kumar Singh
Keyword(s):  
Rate Of Convergence ◽  
Maximal Function ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Test Functions ◽  
Approximation Properties ◽  
Baskakov Operators ◽  
Convergence Behaviour ◽  
Durrmeyer Variant ◽  
Lipschitz Type Maximal Function

<p style='text-indent:20px;'>The aim of this paper is to study some approximation properties of the Durrmeyer variant of <inline-formula><tex-math id="M2">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-Baskakov operators <inline-formula><tex-math id="M3">\begin{document}$ M_{n,\alpha} $\end{document}</tex-math></inline-formula> proposed by Aral and Erbay [<xref ref-type="bibr" rid="b3">3</xref>]. We study the error in the approximation by these operators in terms of the Lipschitz type maximal function and the order of approximation for these operators by means of the Ditzian-Totik modulus of smoothness. The quantitative Voronovskaja and Gr<inline-formula><tex-math id="M4">\begin{document}$ \ddot{u} $\end{document}</tex-math></inline-formula>ss Voronovskaja type theorems are also established. Next, we modify these operators in order to preserve the test functions <inline-formula><tex-math id="M5">\begin{document}$ e_0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ e_2 $\end{document}</tex-math></inline-formula> and show that the modified operators give a better rate of convergence. Finally, we present some graphs to illustrate the convergence behaviour of the operators <inline-formula><tex-math id="M7">\begin{document}$ M_{n,\alpha} $\end{document}</tex-math></inline-formula> and show the comparison of its rate of approximation vis-a-vis the modified operators.</p>

Durrmeyer variant of q-Favard-Szász operators based on Appell polynomials

2017 ◽  
Vol 26 (1) ◽  
pp. 9-17
Author(s):  
P. N. Agrawal ◽  
◽  
Pooja Gupta ◽  
Keyword(s):  
Polynomial Growth ◽  
Weighted Space ◽  
Degree Of Approximation ◽  
Approximation Properties ◽  
Appell Polynomials ◽  
Weighted Modulus Of Continuity ◽  
Szász Operators ◽  
Weighted Modulus ◽  
Durrmeyer Variant ◽  
Lipschitz Type Maximal Function

Karaisa [Karaisa, A., Approximation by Durrmeyer type Jakimoski Leviatan operators, Math. Method. Appl. Sci., DOI: 10.1002/mma.3650 (2015)] introduced the Durrmeyer type variant of Jakimovski-Leviatan operators based on Appell polynomials and studied some approximation properties. The aim of the present paper is to define the q analogue of these operators and establish the rate of convergence for a Lipschitz type space and a Lipschitz type maximal function for the Durrmeyer type variant of these operators. Also, we study the degree of approximation of these operators in a weighted space of polynomial growth and by means of weighted modulus of continuity

Modified algorithm for fast bandwidth selection for kernel estimates of multidimensional probability densities

2020 ◽  
pp. 9-13
Author(s):  
A. V. Lapko ◽  
V. A. Lapko
Keyword(s):  
Probability Density ◽  
Optimal Parameter ◽  
Random Variables ◽  
Kernel Functions ◽  
Independent Random Variables ◽  
Functional Dependencies ◽  
Approximation Properties ◽  
Probability Density Estimation ◽  
Multidimensional Probability ◽  
Selection Of

An original technique has been justified for the fast bandwidths selection of kernel functions in a nonparametric estimate of the multidimensional probability density of the Rosenblatt–Parzen type. The proposed method makes it possible to significantly increase the computational efficiency of the optimization procedure for kernel probability density estimates in the conditions of large-volume statistical data in comparison with traditional approaches. The basis of the proposed approach is the analysis of the optimal parameter formula for the bandwidths of a multidimensional kernel probability density estimate. Dependencies between the nonlinear functional on the probability density and its derivatives up to the second order inclusive of the antikurtosis coefficients of random variables are found. The bandwidths for each random variable are represented as the product of an undefined parameter and their mean square deviation. The influence of the error in restoring the established functional dependencies on the approximation properties of the kernel probability density estimation is determined. The obtained results are implemented as a method of synthesis and analysis of a fast bandwidths selection of the kernel estimation of the two-dimensional probability density of independent random variables. This method uses data on the quantitative characteristics of a family of lognormal distribution laws.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

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.

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