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 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 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 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.

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.

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.

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 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 Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

2013 ◽  
Vol 21 (3) ◽  
pp. 209-222 ◽  
Author(s):  
Ali Olgun ◽  
H. Gül İnce ◽  
Fatma Tasdelen
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Generating Functions ◽  
Type Theorem ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Korovkin Type Theorem

Abstract In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0;A] ; 0 < A < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.

scholarly journals On approximation of Bernstein–Chlodowsky–Gadjiev type operators that fix $e^{-2x}$

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Feyza Tanberk Okumuş ◽  
Mahmut Akyiğit ◽  
Khursheed J. Ansari ◽  
Fuat Usta
Keyword(s):  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Type Theorem ◽  
Function Spaces ◽  
Moduli Of Continuity ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
Different Types ◽  
Theoretical Results

Abstractthat fix the function $e^{-2x} $ e − 2 x for $x\geq 0 $ x ≥ 0 . Then, we provide the approximation properties of these newly defined operators for different types of function spaces. In addition, we focus on the rate of convergence utilizing appropriate moduli of continuity. Then, we provide the Voronovskaya-type theorem for these new operators. Finally, in order to validate our theoretical results, we provide some numerical experiments that are produced by a MATLAB complier.

scholarly journals On approximation properties of Baskakov-Schurer-Szász-Stancu operators based on q-integers

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1359-1378 ◽  
Author(s):  
M. Mursaleen ◽  
A.A.H. Al-Abied ◽  
Khursheed Ansari
Keyword(s):  
Rate Of Convergence ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Approximation Properties ◽  
Stancu Operators ◽  
Voronovskaya Type Theorem ◽  
Lipschitz Type Maximal Function

In the present paper, we introduce Stancu type generalization of Baskakov-Schurer-Sz?sz operators based on the q-integers and investigate their approximation properties. We obtain rate of convergence, weighted approximation and Voronovskaya type theorem for new operators. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Furthermore, we study A-statistical convergence of these operators and also, in order to obtain a better approximation.

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