Korovkin-type theorems and their statistical versions in grand Lebesgue spaces
TURKISH JOURNAL OF MATHEMATICS, vol.44, no.3, pp.1027-1041, 2020 (SCI-Expanded, Scopus, TRDizin)
- 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 (SCI-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
- Open Archive Collection: AVESIS Open Access Collection
- Yıldız Technical University Affiliated: Yes
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.