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Fractional type multivariate sampling operators

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper we introduce a novel extension of sampling operators by replacing the sample values \((f(k/w))_{k=0}^{n}\) with its fractional average (mean) value in n-dimensional parallelepiped. Using the Riemann–Liouville fractional integral operator of order \(\alpha \), we define fractional type multivariate sampling operators based upon a suitable kernel function. Moreover, we give convergence results for these operators in \(C(\mathbf{R}^n)\) and Orlicz spaces and obtain multivariate Voronovskaya type asymptotic formula by means of Euler-Beta functions. Finally, several graphical and numerical results are presented to demonstrate the accuracy, applicability and efficiency of the operators through special kernels.

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  1. Uğur Kadak

    Present address: , Yaşamkent Street, Bolu, 14100, Turkey

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  1. Gazi University, Ankara, 06100, Turkey

    Uğur Kadak

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Kadak, U. Fractional type multivariate sampling operators. RACSAM 115, 153 (2021). https://doi.org/10.1007/s13398-021-01094-4

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