Summability on Mellin-type nonlinear integral operators

ASLAN İ., Duman O.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, cilt.30, sa.6, ss.492-511, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 6
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1080/10652469.2019.1594209
  • Dergi Adı: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.492-511
  • Anahtar Kelimeler: Summability process, nonlinear integral operators, convolution-type integral operators, Mellin-type integral operators, bounded variation, CONVERGENCE, APPROXIMATION
  • Hacettepe Üniversitesi Adresli: Evet

Özet

In this study, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the summability methods defined by Bell. Considering the Haar measure with variation semi-norm in Tonelli's sense, we approach to the functions of bounded variation. Similar results are also obtained for uniformly continuous and bounded functions. Using suitable function classes we investigate the rate of convergence in the approximation. Finally, we give a non-trivial application verifying our approach.