Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2003-21
Keywords
Grand Lebesgue space, Korovkin theorems, shift operator, statistical convergence, positive linear operator, approximation process
First Page
1027
Last Page
1041
Recommended Citation
ZEREN, Y, ISMAILOV, M, & KARAÇAM, C (2020). Korovkin-type theorems and their statistical versions in grand Lebesgue spaces. Turkish Journal of Mathematics 44 (3): 1027-1041. https://doi.org/10.3906/mat-2003-21
