GENERALIZED BERNSTEIN-KANTOROVICH OPERATORS OF BLENDING TYPE

Mathematica Software ◽

Kantorovich Operators ◽

Appl Math

In this note, we derive some approximation properties of the generalized Bernstein-Kantorovich type operators based on two nonnegative parameters considered by A. Kajla [Appl. Math. Comput. 2018]. We establish Voronovskaja type asymptotic theorem for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also derived. Finally, we show the convergence of the operators by illustrative graphics in Mathematica software to certain functions.

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

Carpathian Journal of Mathematics ◽

10.37193/cjm.2018.03.11 ◽

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 ◽

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

Georgian Mathematical Journal ◽

10.1515/gmj-2016-0057 ◽

2018 ◽

Vol 25 (3) ◽

pp. 397-407 ◽

Cited By ~ 20

Author(s):

Hatice Gul Ince Ilarslan ◽

Tuncer Acar

Keyword(s):

Uniform Convergence ◽

Rate Of Convergence ◽

Modulus Of Continuity ◽

Korovkin Theorem ◽

Central Moments ◽

The Korovkin Theorem ◽

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.

Approximation by generalized positive linear Kantorovich operators

Filomat ◽

10.2298/fil1714353d ◽

2017 ◽

Vol 31 (14) ◽

pp. 4353-4368 ◽

Cited By ~ 1

Author(s):

Minakshi Dhamija ◽

Naokant Deo

Keyword(s):

Rate Of Convergence ◽

Approximation Theorem ◽

Weighted Approximation ◽

Local Approximation ◽

Continuous Functions ◽

Absolutely Continuous Functions ◽

Absolutely Continuous ◽

Derivatives Of ◽

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.

Approximation properties of the new type generalized Bernstein-Kantorovich operators

AIMS Mathematics ◽

10.3934/math.2022212 ◽

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 ◽

Voronovskaya Type Theorem ◽

New Type ◽

<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>

Approximation properties of Kantorovich type q-Balázs-Szabados operators

Demonstratio Mathematica ◽

10.1515/dema-2019-0002 ◽

2019 ◽

Vol 52 (1) ◽

pp. 10-19 ◽

Cited By ~ 1

Author(s):

Esma Yıldız Özkan

Keyword(s):

Rate Of Convergence ◽

Approximation Theorem ◽

Local Approximation ◽

Statistical Approximation ◽

AbstractIn this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK operators.

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

Journal of Function Spaces ◽

10.1155/2021/6683004 ◽

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 ◽

Voronovskaja Type Theorem ◽

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.

Rate of approximation for the Bézier variant of Balazs Kantorovich operators

Mathematica Slovaca ◽

10.2478/s12175-007-0029-0 ◽

2007 ◽

Vol 57 (4) ◽

Cited By ~ 8

Author(s):

Vijay Gupta ◽

X. Zeng

Keyword(s):

Rate Of Convergence ◽

Bounded Variation ◽

Functions Of Bounded Variation ◽

Rate Of Approximation ◽

Kantorovich Operators ◽

Bézier Variant

AbstractIn the present paper we study the Bézier variant of the well known Balazs-Kantorovich operators L n,α(f,x), α ≥ 1. We establish the rate of convergence for functions of bounded variation. For particular value α = 1, our main theorem completes a result due to Agratini [Math. Notes (Miskolc) 2 (2001), 3–10].

Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.3827 ◽

2005 ◽

Vol 2005 (23) ◽

pp. 3827-3833 ◽

Cited By ~ 14

Author(s):

Vijay Gupta ◽

Ulrich Abel ◽

Mircea Ivan

Keyword(s):

Rate Of Convergence ◽

Bounded Variation ◽

Continuous Functions ◽

Function Of Bounded Variation ◽

Absolutely Continuous Functions ◽

Absolutely Continuous ◽

Derivatives Of

We study the approximation properties of beta operators of second kind. We obtain the rate of convergence of these operators for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

Generalized Baskakov Kantorovich operators

Filomat ◽

10.2298/fil1719131a ◽

2017 ◽

Vol 31 (19) ◽

pp. 6131-6151

Author(s):

P.N. Agrawal ◽

Meenu Goyal

Keyword(s):

Rate Of Convergence ◽

Bounded Variation ◽

Statistical Convergence ◽

Simultaneous Approximation ◽

Weighted Approximation ◽

Function Of Bounded Variation ◽

Convergence Properties ◽

Almost Everywhere ◽

Direct Results ◽

In this paper, we construct generalized Baskakov Kantorovich operators. We establish some direct results and then study weighted approximation, simultaneous approximation and statistical convergence properties for these operators. Finally, we obtain the rate of convergence for functions having a derivative coinciding almost everywhere with a function of bounded variation for these operators.

Integral modification of Apostol-Genocchi operators

Filomat ◽

10.2298/fil2108533n ◽

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 ◽

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.