Fractional type multivariate sampling operators

Kadak U.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, cilt.115, sa.3, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 115 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s13398-021-01094-4
  • Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Fractional calculus, Multivariate sampling series, Signal-image processing, Neural network, Order of approximation, Voronovskaya type asymptotic formula, Orlicz spaces, MODULAR FUNCTION-SPACES, APPROXIMATION PROPERTIES, INTEGRAL-OPERATORS, CONVERGENCE, CALCULUS, MODEL, SUMMABILITY, ALGORITHM, FORMULAS, SIGNALS
  • Gazi Üniversitesi Adresli: Evet

Özet

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.