scholarly journals Stancu-variant of generalized Baskakov operators

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2625-2632 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Baskakov Operators ◽  
Direct Estimate ◽  
Voronovskaya Type Theorem

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

Modified Lupaş-Jain operators

2020 ◽  
Vol 70 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Murat Bodur
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Order Of Approximation ◽  
Weighted Modulus Of Continuity ◽  
Quantitative Form ◽  
Voronovskaya Type Theorem ◽  
Weighted Modulus

Abstract The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

scholarly journals Approximation properties of the new type generalized Bernstein-Kantorovich operators

2021 ◽  
Vol 7 (3) ◽  
pp. 3826-3844
Author(s):  
Mustafa Kara ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Type Theorem ◽  
Numerical Results ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
New Type ◽  
Kantorovich Operators

<abstract><p>In this paper, we introduce new type of generalized Kantorovich variant of $ \alpha $-Bernstein operators and study their approximation properties. We obtain estimates of rate of convergence involving first and second order modulus of continuity and Lipschitz function are studied for these operators. Furthermore, we establish Voronovskaya type theorem of these operators. The last section is devoted to bivariate new type $ \alpha $-Bernstein-Kantorovich operators and their approximation behaviors. Also, some graphical illustrations and numerical results are provided.</p></abstract>

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>

A note on Baskakov operators based on a function ϑ

2016 ◽  
Vol 25 (1) ◽  
pp. 15-27
Author(s):  
DIDEM AYDIN ARI ◽  
◽  
ALI ARAL ◽  
DANIEL CARDENAS-MORALES ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Modulus Of Continuity ◽  
Shape Preserving ◽  
Baskakov Operators ◽  
Qualitative And Quantitative ◽  
First Order ◽  
Voronovskaya Type Theorem ◽  
Monotonic Convergence ◽  
Weighted Modulus

In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovkin results are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of ϑ-convexity are used throughout the paper

scholarly journals APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV GAMMA OPERATORS

2021 ◽  
pp. 125
Author(s):  
Seda Arpagus ◽  
Ali Olgun
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Gamma Operator ◽  
Voronovskaya Type Theorem

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.

scholarly journals Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. A. Mohiuddine
Keyword(s):  
Rate Of Convergence ◽  
Differentiable Function ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Mixed Modulus Of Smoothness ◽  
Voronovskaja Type Theorem ◽  
Gbs Operators ◽  
Mixed Modulus ◽  
Boolean Sum

AbstractWe construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.

scholarly journals Approximation properties of modified Jain-Gamma operators

2021 ◽  
Vol 13 (3) ◽  
pp. 651-665
Author(s):  
S. Erdogan ◽  
A. Olgun
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Gamma Operator ◽  
Voronovskaya Type Theorem

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

scholarly journals Generalized p,q-Gamma-type operators

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wen-Tao Cheng ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.

scholarly journals Direct Estimate for Some Operators of Durrmeyer Type in Exponential Weighted Space

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Grażyna Krech ◽  
Eugeniusz Wachnicki
Keyword(s):  
Weighted Space ◽  
Type Theorem ◽  
Approximation Order ◽  
Direct Estimate ◽  
Voronovskaya Type Theorem ◽  
Durrmeyer Type Operators

AbstractIn the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.

scholarly journals Stancu-type generalizations of the Chan-Chyan-Srivastava operators

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3733-3742 ◽  
Author(s):  
Gürhan İçöz ◽  
Bayram Çekim
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Modulus Of Smoothness ◽  
Lipschitz Class ◽  
Type Result ◽  
Approximation Theorems

We give the Stancu-type generalization of the operators which is given by Erkus-Duman and Duman in this study. We derive approximation theorems via A-statistical Korovkin-type result. We also give rate of convergence of the operators via the modulus of smoothness, the modulus of continuity, and Lipschitz class functional.

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