Direct and Inverse Results for Kantorovich Type Exponential Sampling Series

In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series ( I w χ ) w > 0 . Further, we establish a representation formula and an inverse result of approx...

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Vydáno v:Resultate der Mathematik Ročník 75; číslo 3
Hlavní autoři: Angamuthu, Sathish Kumar, Bajpeyi, Shivam
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.09.2020
Témata:
Mathematics
Mathematics and Statistics
logarithmic modulus of continuity
inverse result
41A35
30D10
41A25
Kantorovich type exponential sampling series
mellin transform
pointwise convergence
94A20
ISSN:1422-6383, 1420-9012
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Popis
Shrnutí:In this article, we analyse the behaviour of the new family of Kantorovich type exponential sampling series. We derive the point-wise approximation theorem and Voronovskaya type theorem for the series ( I w χ ) w > 0 . Further, we establish a representation formula and an inverse result of approximation for these operators. Finally, we give some examples of kernel functions to which the theory can be applied along with the graphical representation.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-020-01241-0