Approximation properties of Ibragimov-Gadjiev-Durrmeyer operators on Lp (R+)

• Autorzy: Ulusoy G. , Aral A.

Identyfikatory

DOI

10.1515/dema-2017-0017

• Języki publikacji: EN

Abstrakty

EN

We deal with the approximation properties of a new class of positive linear Durrmeyer type operators which offer a reconstruction of integral type operators including well known Durrmeyer operators. This reconstruction allows us to investigate approximation properties of the Durrmeyer operators at the same time. It is first shown that these operators are a positive approximation process in Lp (R+). While we are showing this property of the operators we consider the Ditzian-Totik modulus of smoothness and corresponding K-functional. Then, weighted norm convergence, whose proof is based on Korovkin type theorem on Lp (R+), is given. At the end of the paper we show several examples of classical sequences that can be obtained from the Ibragimov-Gadjiev-Durrmeyer operators.

Słowa kluczowe

EN

Durrmeyer operators; Ibragimov-Gadjiev operators; modulus of continuity; Lp approximation

PL

operatory Durrmeyera; operatory Ibragimova-Gadjiewa; moduł ciągłości; przybliżenie Lp

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 156--174
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Ulusoy G.

• Department of Mathematics, Çankırı Karatekin University, TR-18100, Çankırı, Turkey

autor

Aral A.

• Department of Mathematics, Kırıkkale University, TR-71450, Kirikkale, Turkey

Bibliografia

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• [12] Aral A., Acar T., Modern mathematical methods and high performance computing in science and technology, 1–15, Springer Proc. Math. Stat., 171, (Springer, Singapore, 2016)
• [13] Ditzian, Z., Totik, V., Moduli of Smoothness, Springer Series in Computational Mathematics 9, (Springer-Verlag, Berlin, Heidelberg, Newyork, 1987)
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Uwagi

PL

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