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 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.

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 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.

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 Convergence properties of Ibragimov-Gadjiev-Durrmeyer operators

2015 ◽  
Vol 24 (1) ◽  
pp. 17-26
Author(s):  
EMRE DENIZ ◽  
◽  
ALI ARAL ◽  
Keyword(s):  
Weighted Space ◽  
Type Theorem ◽  
Approximation Error ◽  
Weighted Norm ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Korovkin Type Theorem ◽  
Durrmeyer Operators ◽  
Weighted Modulus ◽  
Direct Approximation

The purpose of the present paper is to study the local and global direct approximation properties of the Durrmeyer type generalization of Ibragimov Gadjiev operators defined in [Aral, A. and Acar, T., On Approximation Properties of Generalized Durrmeyer Operators, (submitted)]. The results obtained in this study consist of Korovkin type theorem which enables us to approximate a function uniformly by new Durrmeyer operators, and estimate for approximation error of the operators in terms of weighted modulus of continuity. These results are obtained for the functions which belong to weighted space with polynomial weighted norm by new operators which act on functions defined on the non compact interval [0.∞). We finally present a direct approximation result.

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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