scholarly journals Integral modification of Apostol-Genocchi operators

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2533-2544
Author(s):  
N Neha ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Absolute Error ◽  
Local Approximation ◽  
Approximation Properties ◽  
Type Space ◽  
Durrmeyer Operators ◽  
Genocchi Polynomials ◽  
The Absolute ◽  
Mathematica Software

In this article, we consider Jain-Durrmeyer operators associated with the Apostol-Genocchi polynomials and study the approximation properties of these Durrmeyer operators. Furthermore, we examine the approximation behaviour of these operators including K-functional. We estimate the rate of convergence of the proposed operators for function in Lipschitz-type space and local approximation results by using modulus of continuity. Employing Mathematica software, to show the approximation and the absolute error graphically by varying the values of given parameters.

scholarly journals Approximation Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhi-Peng Lin ◽  
Wen-Tao Cheng ◽  
Xiao-Wei Xu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Gamma Function ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Central Moments ◽  
Durrmeyer Operators

In this article, we introduce a new Durrmeyer-type generalization of p , q -Szász-Mirakjan operators using the p , q -gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K -functional. Finally, the rate of convergence and weighted approximation of these operators are presented.

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 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.

Some approximation properties of a kind of (p, q)-Phillips operators

2019 ◽  
Vol 69 (6) ◽  
pp. 1381-1394
Author(s):  
Wentao Cheng ◽  
Chunyan Gui ◽  
Yongmo Hu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Phillips Operators

Abstract In this paper, a kind of new analogue of Phillips operators based on (p, q)-integers is introduced. The moments of the operators are established. Then some local approximation for the above operators is discussed. Also, the rate of convergence and weighted approximation by these operators by means of modulus of continuity are studied. Furthermore, the Voronovskaja type asymptotic formula is investigated.

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.

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

Approximation by bivariate (p,q)-Baskakov–Kantorovich operators

2018 ◽  
Vol 25 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Hatice Gul Ince Ilarslan ◽  
Tuncer Acar
Keyword(s):  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Korovkin Theorem ◽  
Central Moments ◽  
The Korovkin Theorem ◽  
Kantorovich Operators

AbstractThe present paper deals with the bivariate{(p,q)}-Baskakov–Kantorovich operators and their approximation properties. First we construct the operators and obtain some auxiliary results such as calculations of moments and central moments, etc. Our main results consist of uniform convergence of the operators via the Korovkin theorem and rate of convergence in terms of modulus of continuity.

scholarly journals Approximation by generalized positive linear Kantorovich operators

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4353-4368 ◽  
Author(s):  
Minakshi Dhamija ◽  
Naokant Deo
Keyword(s):  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Derivatives Of ◽  
Kantorovich Operators

In the present article, we introduce generalized positive linear-Kantorovich operators depending on P?lya-Eggenberger distribution (PED) as well as inverse P?lya-Eggenberger distribution (IPED) and for these operators, we study some approximation properties like local approximation theorem, weighted approximation and estimation of rate of convergence for absolutely continuous functions having derivatives of bounded variation.

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>

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