Quantitative Estimates for Nonlinear Sampling Kantorovich Operators


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Çetin N., Costarelli D., Vinti G.

Results in Mathematics, cilt.76, sa.2, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00025-021-01383-9
  • Dergi Adı: Results in Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Nonlinear sampling Kantorovich operators, Orlicz spaces, modulus of smoothness, quantitative estimates, Lipschitz classes, INTEGRAL-OPERATORS, APPROXIMATION, CONVERGENCE, ORDER
  • Ankara Hacı Bayram Veli Üniversitesi Adresli: Hayır

Özet

© 2021, The Author(s).In this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in Lp-spaces, 1 ≤ p< ∞, and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the Lp-case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.