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.

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 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 generalized integral Favard-Szász type operators involving Sheffer polynomials

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1921-1935
Author(s):  
Seda Karateke ◽  
Çiğdem Atakut ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Modulus Of Continuity ◽  
Order Of Convergence ◽  
Type Theorem ◽  
Type Operator ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Integral Type ◽  
Korovkin Type Theorem ◽  
Numerical Examples ◽  
Sheffer Polynomials

This article deals with the approximation properties of a generalization of an integral type operator in the sense of Favard-Sz?sz type operators including Sheffer polynomials with graphics plotted using Maple. We investigate the order of convergence, in terms of the first and the second order modulus of continuity, Peetre?s K-functional and give theorems on convergence in weighted spaces of functions by means of weighted Korovkin type theorem. At the end of the work, we give some numerical examples.

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 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.

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 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 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 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 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.

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