scholarly journals On bivariate Jain operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Münüse Akçay ◽  
Gülen Başcanbaz-Tunca
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Elementary Method ◽  
Voronovskaja Type Theorem

<p style='text-indent:20px;'>In this paper we deal with bivariate extension of Jain operators. Using elementary method, we show that these opearators are non-increasing in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> when the attached function is convex. Moreover, we demonstrate that these operators preserve the properties of modulus of continuity. Finally, we present a Voronovskaja type theorem for the sequence of bivariate Jain operators.</p>

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 Dunkl generalization of q-Szász-Mirakjan operators which preserve x2

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 733-747 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Shagufta Rahman
Keyword(s):  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem

In the present paper we construct q-Sz?sz-Mirakjan operators generated by Dunkl generalization of the exponential function which preserve x2. We obtain some approximation results via universal Korovkin?s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain a Voronovskaja type theorem for these operators.

scholarly journals On Stancu-Type Generalization of Modified p , q -Szász-Mirakjan-Kantorovich Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yong-Mo Hu ◽  
Wen-Tao Cheng ◽  
Chun-Yan Gui ◽  
Wen-Hui Zhang
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Voronovskaja Type Theorem ◽  
Kantorovich Operators

In the present article, we construct p , q -Szász-Mirakjan-Kantorovich-Stancu operators with three parameters λ , α , β . First, the moments and central moments are estimated. Then, local approximation properties of these operators are established via K -functionals and Steklov mean in means of modulus of continuity. Also, a Voronovskaja-type theorem is presented. Finally, the pointwise estimates, rate of convergence, and weighted approximation of these operators are studied.

scholarly journals The generalization of certain results for Szasz-Mirakjan-Schurer operators

2012 ◽  
Vol 21 (1) ◽  
pp. 79-85
Author(s):  
DAN MICLAUS ◽  
◽  
OVIDIU T. POP ◽  
Keyword(s):  
Uniform Convergence ◽  
Present Article ◽  
General Formula ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Order Of Approximation ◽  
Test Functions ◽  
Voronovskaja Type Theorem

The present article continues earlier research by authors, in order to reach two goals. Firstly, we give a general formula concerning calculation of the test functions by Szasz-Mirakjan-Schurer operators and secondly, we establish a Voronovskaja type theorem, the uniform convergence and the ´ order of approximation using the modulus of continuity for the same operators.

scholarly journals Approximation properties of modified q-gamma operators preserving linear functions

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1601-1609
Author(s):  
Wen-Tao Cheng ◽  
Wen-Hui Zhang ◽  
Jing Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Gamma Functions ◽  
Voronovskaja Type Theorem

In this paper, we introduce the q-analogue of modified Gamma operators preserving linear functions. We establish the moments of the operators using the q-Gamma functions. Next, some local approximation for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Furthermore, we obtain the Voronovskaja type theorem.

scholarly journals Approximation Properties of λ -Gamma Operators Based on q -Integers

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Wen-Tao Cheng ◽  
Xiao-Jun Tang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, we will introduce λ -Gamma operators based on q -integers. First, the auxiliary results about the moments are presented, and the central moments of these operators are also estimated. Then, we discuss some local approximation properties of these operators by means of modulus of continuity and Peetre K -functional. And the rate of convergence and weighted approximation for these operators are researched. Furthermore, we investigate the Voronovskaja type theorems including the quantitative q -Voronovskaja type theorem and q -Grüss-Voronovskaja 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 Approximation by Genuineq-Bernstein-Durrmeyer Polynomials in Compact Disks in the Caseq>1

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nazim I. Mahmudov
Keyword(s):  
Open Problem ◽  
Analytic Functions ◽  
Type Theorem ◽  
Linear Operators ◽  
Explicit Formulas ◽  
Rate Of Approximation ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

This paper deals with approximating properties of the newly definedq-generalization of the genuine Bernstein-Durrmeyer polynomials in the caseq>1, which are no longer positive linear operators onC0,1. Quantitative estimates of the convergence, the Voronovskaja-type theorem, and saturation of convergence for complex genuineq-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that, for functions analytic inz∈ℂ:z<R,R>q, the rate of approximation by the genuineq-Bernstein-Durrmeyer polynomialsq>1is of orderq−nversus1/nfor the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuineq-Bernstein-Durrmeyer forq>1. This paper represents an answer to the open problem initiated by Gal in (2013, page 115).

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