Korovkin-type theorems and their statistical versions in grand Lebesgue spaces


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Zeren Y. , Ismaılov M., Karaçam C.

Turkish Journal Of Mathematics, vol.44, no.3, pp.1027-1041, 2020 (Journal Indexed in SCI)

  • Publication Type: Article / Article
  • Volume: 44 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-2003-21
  • Title of Journal : Turkish Journal Of Mathematics
  • Page Numbers: pp.1027-1041

Abstract

The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace G p) (−π; π) of grand Lebesgue space is defined using shift operator. It is shown that the space of infinitely differentiable finite functions is dense in G p) (−π; π). The analogs of Korovkin theorems are proved in G p) (−π; π). These results are established in G p) (−π; π) in the sense of statistical convergence. The obtained results are applied to a sequence of operators generated by the Kantorovich polynomials, to Fejer and Abel-Poisson convolution operators.