Parametric Extension of a Certain Family of Summation-Integral Type Operators-Reference-Cited by-同舟云学术

Parametric Extension of a Certain Family of Summation-Integral Type Operators

Published:2023-06-30 Issue:2 Volume:44 Page:315-327
ISSN:2587-2680
Container-title:Cumhuriyet Science Journal
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Author:

ODABAŞI Nadire Fulda¹^ORCID,YÜKSEL İsmet²^ORCID

Affiliation:

1. GAZİ ÜNİVERSİTESİ, FEN BİLİMLERİ ENSTİTÜSÜ

2. GAZİ ÜNİVERSİTESİ, FEN FAKÜLTESİ

Abstract

In this paper, we introduce a parametric extension of a certain family of summation-integral type operators on the interval [0,∞). Firstly, we obtain test functions and central moments. Secondly, we investigate weighted approximation properties for these operators and estimate the rate of convergence. Then, we give a pointwise approximation for the Peetre K-functional and functions of the Lipschitz class. Moreover, we demonstrate Voronovskaja type theorem for the operators. Finally, the convergence properties of operators to some functions are illustrated by graphics.

Publisher

Cumhuriyet University

Subject

General Medicine

Reference38 articles.

1. [1] Weierstrass K., Uber die analytische Darstellbarkeit sogenannter willkurlicher Functionen einer reellen Veranderlichen Sitzungsberichteder, Koniglich Preussischen Akedemie der Wissenschcaften zu Berlin, (1885) 633-639, 789-805.

2. [2] Baskakov V.A., An instance of sequance of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR (N.S.), 113 (1957) 249-251.

3. [3] Durrmeyer J.L., Une Formule de d’inversion de la transform’ee de Laplace: applications`a la th’eorie des moments, These de 3e cycle, Facult’e des Sciences de I’Universit’e de Paris, (1967).

4. [4] May C.P., On Phillips operator, J. Approximation Theory, 20(4) (1977) 315–332.

5. [5] Srivastava H.M., Gupta V., A certain family of summation-integral type operators, Math. Comput. Modelling, 37(12-13) (2003) 1307-1315.