scholarly journals A genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2611-2623 ◽  
Author(s):  
Trapti Neer ◽  
P.N. Agrawal
Keyword(s):  
Approximation Theorem ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Global Approximation ◽  
Approximation Of Functions ◽  
Moment Estimates ◽  
Durrmeyer Type Operators ◽  
Direct Results ◽  
Classical Modulus

In this paper, we construct a genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions. We establish some moment estimates and the direct results which include global approximation theorem in terms of classical modulus of continuity, local approximation theorem in terms of the second order Ditizian-Totik modulus of smoothness, Voronovskaya-type asymptotic theorem and a quantitative estimate of the same type. Lastly, we study the approximation of functions having a derivative of bounded variation.

scholarly journals Bezier variant of genuine-Durrmeyer type operators based on Polya distribution

2017 ◽  
Vol 33 (1) ◽  
pp. 73-86
Author(s):  
TRAPTI NEER ◽  
◽  
ANA MARIA ACU ◽  
P. N. AGRAWAL ◽  
◽  
...  
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Global Approximation ◽  
Voronovskaja Type Theorem ◽  
Polya Distribution ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In this paper we introduce the Bezier variant of genuine-Durrmeyer type operators having Polya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness. The rate of convergence for functions whose derivatives are of bounded variation is obtained. Further, we show the rate of convergence of these operators to certain functions by illustrative graphics using the Maple algorithms.

scholarly journals Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 316 ◽  
Author(s):  
Hari Srivastava ◽  
Faruk Özger ◽  
S. Mohiuddine
Keyword(s):  
Uniform Convergence ◽  
Shape Parameter ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Bernstein Operators ◽  
Global Approximation ◽  
Approximation Result ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Direct Approximation

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ - 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.

scholarly journals On Approximation by Gupta type general family of Operators

2021 ◽  
Author(s):  
Karunesh Singh
Keyword(s):  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Asymptotic Result ◽  
Linear Positive Operators ◽  
Type Approximation ◽  
Quantitative Form ◽  
Wide Range ◽  
Direct Results

In this paper, we study Gupta type family of positive linear operators, which have a wide range of many well known linear positive operators e.g. Phillips, Baskakov-Durrmeyer, Baskakov-Sz\’{a}sz, Sz\’{a}sz-Beta, Lupa\c{s}-Beta, Lupa\c{s}-Sz\’{a}sz, genuine Bernstein-Durrmeyer, Link, P\u{a}lt\u{a}nea, Mihe\c{s}an-Durrmeyer, link Bernstein-Durrmeyer etc. We first establish direct results in terms of usual modulus of continuity having order 2 and Ditzian-Totik modulus of smoothness and then study quantitative Voronovkaya theorem for the weighted spaces of functions. Further, we establish Gr\“{u}ss-Voronovskaja type approximation theorem and also derive Gr\”{u}ss-Voronovskaja type asymptotic result in quantitative form.

scholarly journals Bézier variant of the Szász-Durrmeyer type operators based on the Poisson-Charlier polynomials

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3265-3273
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Charlier Polynomials ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In the present paper we introduce the B?zier variant of the Sz?sz-Durrmeyer type operators, involving the Poisson-Charlier polynomials. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness and the rate of convergence for differential functions whose derivatives are of bounded variation.

scholarly journals Better degree of approximation by modified Bernstein-Durrmeyer type operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Purshottam Narain Agrawal ◽  
Şule Yüksel Güngör ◽  
Abhishek Kumar
Keyword(s):  
Present Article ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Bernstein Operators ◽  
Approximation Of Functions ◽  
Careful Choice ◽  
Durrmeyer Type Operators ◽  
Durrmeyer Variant ◽  
Derivatives Of ◽  
Infinitely Differentiable Function

<p style='text-indent:20px;'>In the present article we investigate a Durrmeyer variant of the generalized Bernstein-operators based on a function <inline-formula><tex-math id="M1">\begin{document}$ \tau(x), $\end{document}</tex-math></inline-formula> where <inline-formula><tex-math id="M2">\begin{document}$ \tau $\end{document}</tex-math></inline-formula> is infinitely differentiable function on <inline-formula><tex-math id="M3">\begin{document}$ [0, 1], \; \tau(0) = 0, \tau(1) = 1 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \tau^{\prime }(x)&gt;0, \;\forall\;\; x\in[0, 1]. $\end{document}</tex-math></inline-formula> We study the degree of approximation by means of the modulus of continuity and the Ditzian-Totik modulus of smoothness. A Voronovskaja type asymptotic theorem and the approximation of functions with derivatives of bounded variation are also studied. By means of a numerical example, finally we illustrate the convergence of these operators to certain functions through graphs and show a careful choice of the function <inline-formula><tex-math id="M5">\begin{document}$ \tau(x) $\end{document}</tex-math></inline-formula> leads to a better approximation than the generalized Bernstein-Durrmeyer type operators considered by Kajla and Acar [<xref ref-type="bibr" rid="b11">11</xref>].</p>

scholarly journals Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on p , q -Integers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Exponential Function ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators ◽  
Direct Results

In this article, our main purpose is to define the p , q -variant of Szász-Durrmeyer type operators with the help of Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results of the aforementioned operators. Moreover, we establish some approximation results in weighted spaces.

scholarly journals Direct local and global approximation theorem for Bernstein-type operators

Filomat ◽  
2004 ◽  
pp. 27-32 ◽  
Author(s):  
Zoltan Finta
Keyword(s):  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Global Approximation ◽  
Bernstein Type ◽  
Global Estimates

Direct local and global estimates are established for Bernstein - type operators using Ditzian - Totik modulus of smoothness of second order.

scholarly journals General family of exponential operators

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4043-4060
Author(s):  
Km. Lipi ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Direct Approximation ◽  
Derivatives Of

In this article, we deal with the approximation properties of Ismail-May operators [16] based on a non-negative real parameter ?. We provide some graphs and error estimation table for a numerical example depicting the convergence of our proposed operators. We further define the B?zier variant of these operators and give a direct approximation theorem using Ditizan-Totik modulus of smoothness and a Voronovoskaya type asymptotic theorem. We also study the error in approximation of functions having derivatives of bounded variation. Lastly, we introduce the bivariate generalization of Ismail May operators and estimate its rate of convergence for functions of Lipschitz class.

scholarly journals On generalized Baskakov-Durrmeyer-Stancu type operators

2017 ◽  
Vol 50 (1) ◽  
pp. 144-155
Author(s):  
Angamuthu Sathish Kumar ◽  
Zoltán Finta ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Recurrence Relation ◽  
Approximation Property ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Direct Result ◽  
Approximation Properties ◽  
Statistical Approximation

Abstract In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

scholarly journals Approximation Theorem for New Modification of q -Bernstein Operators on (0,1)

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yun-Shun Wu ◽  
Wen-Tao Cheng ◽  
Feng-Lin Chen ◽  
Yong-Hui Zhou
Keyword(s):  
Approximation Theorem ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Central Moment ◽  
Bernstein Operators ◽  
Lipschitz Classes ◽  
Korovkin Type Approximation Theorem ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Quantitative Properties

In this work, we extend the works of F. Usta and construct new modified q -Bernstein operators using the second central moment of the q -Bernstein operators defined by G. M. Phillips. The moments and central moment computation formulas and their quantitative properties are discussed. Also, the Korovkin-type approximation theorem of these operators and the Voronovskaja-type asymptotic formula are investigated. Then, two local approximation theorems using Peetre’s K -functional and Steklov mean and in terms of modulus of smoothness are obtained. Finally, the rate of convergence by means of modulus of continuity and three different Lipschitz classes for these operators are studied, and some graphs and numerical examples are shown by using Matlab algorithms.

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