ON MODIFIED MOMENT-TYPE OPERATORS

2021 ◽  
Vol 10 (12) ◽  
pp. 3669-3677
Author(s):  
Gümrah Uysal
Keyword(s):  
Real Axis ◽  
Exponential Function ◽  
Type Theorem ◽  
Present Moment ◽  
Convergence Theorems ◽  
Voronovskaya Type Theorem

We propose a modification for moment-type operators in order to preserve the exponential function $e^{2cx}$ with $c>0$ on real axis. First, we present moment identities. Then, we prove two weighted convergence theorems. Finally, we present a Voronovskaya-type theorem for the new operators.

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

scholarly journals A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Rabia Aktaş ◽  
Bayram Çekim ◽  
Fatma Taşdelen
Keyword(s):  
Type Theorem ◽  
Approximation Properties ◽  
Szász Operators ◽  
Voronovskaya Type Theorem

We introduce a Kantorovich-Stancu type modification of a generalization of Szasz operators defined by means of the Brenke type polynomials and obtain approximation properties of these operators. Also, we give a Voronovskaya type theorem for Kantorovich-Stancu type operators including Gould-Hopper polynomials.

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.

Periodic Point at Real Axis for a Generalized 3x+1 Function

2011 ◽  
Vol 55-57 ◽  
pp. 1670-1674 ◽  
Author(s):  
Shuai Liu ◽  
Zheng Xuan Wang
Keyword(s):  
Periodic Point ◽  
Real Axis ◽  
Exponential Function ◽  
Periodic Points ◽  
Divergence Points ◽  
Fractal Character ◽  
Convergence And Divergence ◽  
Complex Exponential

In order to study the fractal character of representative complex exponential function just as generalized 3x+1 function T(x). In this essay, we proved that T(x) has periodic points of every period in bound (n, n+1) when n>1 in real axis. Then, we found the distribution of 2-periods points of T(x) in real axis. We put forward the bottom bound of 2-periodic point’s number and proved it. Moreover, we found the number of T(x)’s 2-periodic points in different bounds to validate our conclusion. Then, we extended the conclusion to i-periods points and find similar conclusion. Finally, we proved there exist endless convergence and divergence points of T(x) in real axis.

scholarly journals A Voronovskaya Type Theorem on Modified Post-Widder Operators Preserving x2

2011 ◽  
Vol 51 (1) ◽  
pp. 87-91
Author(s):  
Mohammad Arif Siddiqui ◽  
Raksha Rani Agrawal
Keyword(s):  
Type Theorem ◽  
Voronovskaya Type Theorem

scholarly journals Direct Estimate for Some Operators of Durrmeyer Type in Exponential Weighted Space

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
Grażyna Krech ◽  
Eugeniusz Wachnicki
Keyword(s):  
Weighted Space ◽  
Type Theorem ◽  
Approximation Order ◽  
Direct Estimate ◽  
Voronovskaya Type Theorem ◽  
Durrmeyer Type Operators

AbstractIn the present paper, we investigate the convergence and the approximation order of some Durrmeyer type operators in exponential weighted space. Furthermore, we obtain the Voronovskaya type theorem for these operators.

scholarly journals Dunkl generalization of q-Szász-Mirakjan operators which preserve x2

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 733-747 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Shagufta Rahman
Keyword(s):  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem

In the present paper we construct q-Sz?sz-Mirakjan operators generated by Dunkl generalization of the exponential function which preserve x2. We obtain some approximation results via universal Korovkin?s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain a Voronovskaja type theorem for these operators.

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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