Convergence in Phi-Variation and Rate of Approximation for Nonlinear Integral Operators Using Summability Process

ASLAN İ.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.18, sa.1, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00009-020-01623-2
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Summability process, nonlinear integral operators, convolution-type integral operators, bounded phi-variation, rate of approximation, ACCELERATION, RESPECT
  • Hacettepe Üniversitesi Adresli: Evet

Özet

We investigate the approximation properties of nonlinear integral operators of the convolution type. In this approximation, we use functions of bounded variation based on the appropriate functionals. To get more general results, we consider Bell-type summability methods in the approximation. Moreover, we examine the rate of approximation. Then, using summability methods, we obtain a characterization for absolute continuity. Our examples at the end of the paper clearly demonstrate why we used summability methods rather than convergence in the conventional sense.