TURKISH JOURNAL OF MATHEMATICS, vol.44, no.3, pp.1027-1041, 2020 (SCI-Expanded)
Article / Article
TURKISH JOURNAL OF MATHEMATICS
Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
Grand Lebesgue space, Korovkin theorems, shift operator, statistical convergence, positive linear operator, approximation process, PIECEWISE-LINEAR PHASE, MORREY, CONVERGENCE, SYSTEM, EXPONENTS, BASICITY, HARDY
Yıldız Technical University Affiliated:
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.