On generalized Baskakov-Durrmeyer-Stancu type operators

• Autorzy: Kumar A. S. , Finta Z. , Agrawal P. N.

Identyfikatory

DOI

10.1515/dema-2017-0016

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

Słowa kluczowe

EN

Baskakov-Durrmeyer-Stancu operators; Lipschitz type space; rate of convergence; modulus of smoothness; A-statistical convergence

PL

operatory typu Baskakowa-Durrmeyera-Stancua; przestrzeń typu Lipschitza; szybkość zbieżności; moduł gładkości; konwergencja statystyczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 144--155
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Kumar A. S.

• Department of Mathematics, National Institute of Technology Jalandhar, Jalandhar-144001, India

autor

Finta Z.

• Department of Mathematics, Babeş-Bolyai University, 1, M. Kogălniceanu st., 400084 Cluj-Napoca, Romania

autor

Agrawal P. N.

• Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India

Bibliografia

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• [3] Wafi A., Khatoon S., On the Order of Approximation of Functions by Generalized Baskakov Operators, Indian J. Pure Appl.Math., 2004, 35, 347-358
• [4] Erencin A., Bascanbaz-Tunca G., Approximation Properties of a Class of Linear Positive Operators in Weighted Spaces, C. R. Acad. Bulgare Sci., 2010, 63, 1397-1404
• [5] Wa A., Khatoon S., Convergence and Voronovskaja-Type Theorems for Derivatives of Generalized Baskakov Operators, Cent. Eur. J. Math., 2008, 6, 325-334
• [6] Erencin A., Durrmeyer Type Modication of Generalized Baskakov Operators, Appl. Math. Comput., 2011, 218, 4384-4390
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• [11] Durrmeyer J. L., Une formule d’inversion de la transformée de Laplace: Applications à la théorie des moments, Thèse de 3ème cycle, Faculté des Sciences Univ. Paris, 1967
• [12] Gupta V., Verma D. K., Agrawal P. N., Simultaneous Approximation by Certain Baskakov-Durrmeyer-Stancu Operators, J. Egyptian Math. Soc., 2012, 20, 183-187
• [13] Krech G., Wachnicki E., Direct Estimate for Some Operators of Durrmeyer Type in Exponential Weighted Space, Demonstratio Math., 2014, 47, 336-349
• [14] Malejki R., Wachnicki E., On the Baskakov-Durrmeyer Type Operators, Comment. Math., 2014, 54, 39-49
• [15] Wa A., Khatoon S., Direct and Inverse Theorems for Generalized Baskakov Operators in Polynomial Weighted Space, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat., 2004, 50, 159-173
• [16] Gadjiev A. D., The Convergence Problem for a Sequence of Positive Linear Operators on Unbounded Sets, and Theorems Analogous to that of P. P. Korovkin, Dokl. Akad. Nauk. SSSR., 1974, 218, 1001-1004 [in Russian]; Sov. Math. Dokl., 1974, 15, 1433-1436 [in English]
• [17] Gadjiev A. D., On Korovkin Type Theorems, Math. Zametki, 1976, 20, 781-786
• [18] Gadjiev A. D., Efendiyev R. O., Ibikli E., On Korovkin Type Theorem in the Space of Locally Integrable Functions, Czech. Math. J., 2003, 53, 45-53
• [19] Özarslan M. A., Duman O., Srivastava H. M., Statistical Approximation Results for Kantorovich-Type Operators Involving Some Special Polynomials, Math. Comput. Modelling., 2008, 48, 388-401
• [20] Duman O., Orhan C., Rates of A-Statistical Convergence of Operators in the Space of Locally Integrable Functions, Appl. Math. Lett., 2008, 21, 431-435
• [21] Erkus E., Duman O., Srivastava H. M., Statistical Approximation of Certain Positive Linear Operators Constructed by Means of the Chan-Chyan-Srivastava polynomials, Appl. Math. Comput., 2006, 182, 213-222

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).