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


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ZEREN Y., Ismailov M., Karacam C.

TURKISH JOURNAL OF MATHEMATICS, vol.44, no.3, pp.1027-1041, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.3906/mat-2003-21
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1027-1041
  • Keywords: Grand Lebesgue space, Korovkin theorems, shift operator, statistical convergence, positive linear operator, approximation process, PIECEWISE-LINEAR PHASE, MORREY, CONVERGENCE, SYSTEM, EXPONENTS, BASICITY, HARDY

Abstract

The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace G(p)) (-pi; pi) 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)) (-pi; pi). The analogs of Korovkin theorems are proved in G(p)) (-pi; pi). These results are established in G(p)) (-pi; pi) 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.