REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.115, no.3, 2021 (SCI-Expanded)
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(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.