scholarly journals Bivariate-Schurer-Stancu operators based on (p,q)-integers

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1251-1258 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Uniform Approximation ◽  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Korovkin Type Theorem ◽  
Stancu Operators

The aim of this article is to introduce a bivariate extension of Schurer-Stancu operators based on (p,q)-integers. We prove uniform approximation by means of Bohman-Korovkin type theorem, rate of convergence using total modulus of smoothness and degree of approximation via second order modulus of smoothness, Peetre?s K-functional, Lipschitz type class.

scholarly journals A new kind of Bi-variate $ \lambda $ -Bernstein-Kantorovich type operator with shifted knots and its associated GBS form

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Purshottam Narain Agrawal ◽  
Behar Baxhaku ◽  
Rahul Shukla
Keyword(s):  
Rate Of Convergence ◽  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Type Operator ◽  
Mixed Modulus Of Smoothness ◽  
Voronovskaja Type Theorem ◽  
Differentiable Functions ◽  
Mixed Modulus ◽  
Approximation Of A Function

<p style='text-indent:20px;'>In this paper, we introduce a bi-variate case of a new kind of <inline-formula><tex-math id="M1">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-Bernstein-Kantorovich type operator with shifted knots defined by Rahman et al. [<xref ref-type="bibr" rid="b31">31</xref>]. The rate of convergence of the bi-variate operators is obtained in terms of the complete and partial moduli of continuity. Next, we give an error estimate in the approximation of a function in the Lipschitz class and establish a Voronovskaja type theorem. Also, we define the associated GBS(Generalized Boolean Sum) operators and study the degree of approximation of Bögel continuous and Bögel differentiable functions by these operators with the aid of the mixed modulus of smoothness. Finally, we show the rate of convergence of the bi-variate operators and their GBS case for certain functions by illustrative graphics and tables using MATLAB algorithms.</p>

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 Statistical Korovkin and Voronovskaya type theorem for the Cesaro second-order operator of fuzzy numbers

2020 ◽  
Vol 65 (4) ◽  
pp. 561-574
Author(s):  
Naim L. Braha ◽  
Valdete Loku
Keyword(s):  
Rate Of Convergence ◽  
Fuzzy Numbers ◽  
Type Theorem ◽  
Summability Method ◽  
Second Order ◽  
Order Operator ◽  
Korovkin Type Theorem ◽  
Voronovskaya Type Theorem

In this paper we define the Ces\'aro second-order summability method for fuzzy numbers and prove Korovkin type theorem, then as the application of it, we prove the rate of convergence. In the last section, we prove the kind of Voronovskaya type theorem and give some concluding remarks related to the obtained results.

scholarly journals On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Edmond Aliaga ◽  
Behar Baxhaku
Keyword(s):  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Matlab Software ◽  
Type Space ◽  
Mixed Modulus Of Smoothness ◽  
Mixed Modulus ◽  
Boolean Sum

In this article, we establish an extension of the bivariate generalization of the q -Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q -Bernstein type. For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. For the GBS type operators, we establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate q -Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MATLAB software.

scholarly journals Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 335-343 ◽  
Author(s):  
Arun Kajla ◽  
Serkan Araci
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Smoothness ◽  
Stancu Operators ◽  
Rate Of Approximation ◽  
Type Approximation ◽  
Kantorovich Operators

AbstractIn the paper the authors introduce the Kantorovich variant of Stancu operators based on Pólya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, such as Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are bounded is also obtained.

Jakimovski–Leviatan operators of Kantorovich type involving multiple Appell polynomials

2019 ◽  
Vol 28 (1) ◽  
pp. 73-82 ◽  
Author(s):  
Pooja Gupta ◽  
Ana Maria Acu ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Maximal Function ◽  
Polynomial Growth ◽  
Weighted Space ◽  
Type Theorem ◽  
Degree Of Approximation ◽  
Type Operator ◽  
Appell Polynomials ◽  
Lipschitz Type Maximal Function

Abstract The purpose of the present paper is to obtain the degree of approximation in terms of a Lipschitz type maximal function for the Kantorovich type modification of Jakimovski–Leviatan operators based on multiple Appell polynomials. Also, we study the rate of approximation of these operators in a weighted space of polynomial growth and for functions having a derivative of bounded variation. A Voronvskaja type theorem is obtained. Further, we illustrate the convergence of these operators for certain functions through tables and figures using the Maple algorithm and, by a numerical example, we show that our Kantorovich type operator involving multiple Appell polynomials yields a better rate of convergence than the Durrmeyer type Jakimovski Leviatan operators based on Appell polynomials introduced by Karaisa (2016).

scholarly journals A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 980
Author(s):  
Naim Latif Braha ◽  
Toufik Mansour ◽  
Hari Mohan Srivastava
Keyword(s):  
Type Theorem ◽  
Weighted Spaces ◽  
Shape Preserving ◽  
Korovkin Type Theorem ◽  
Stancu Operators ◽  
New Class ◽  
Approximation Operators ◽  
Voronovskaya Type Theorem ◽  
Shape Preserving Properties ◽  
Special Case

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.

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.

scholarly journals Approximation by Stancu-Durrmeyer type operators based on Pólya-Eggenberger distribution

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4249-4261
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Bounded Variation ◽  
Modulus Of Smoothness ◽  
Stancu Operators ◽  
Rate Of Approximation ◽  
Durrmeyer Type Operators

In the present paper we introduce the Durrmeyer type modification of Stancu operators based on P?lya-Eggenberger distribution. For these new operators some indispensable auxiliary results are established in the second section. Our further study focuses on a Voronovskaja type asymptotic formula and some estimates of the rate of approximation involving modulus of smoothness, respectively Ditzian-Totik modulus of smoothness. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

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.

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