TURKISH JOURNAL OF MATHEMATICS, vol.44, no.3, pp.1027-1041, 2020 (Peer-Reviewed Journal)
Article / Article
TURKISH JOURNAL OF MATHEMATICS
Science Citation Index 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
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.