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Full-Text Articles in Physical Sciences and Mathematics
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Korovkin-Type Theorems And Their Statistical Versions In Grand Lebesgue Spaces, Yusuf Zeren, Miqdad Ismailov, Cemi̇l Karaçam
Turkish Journal of Mathematics
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.
On Basicity Of The System Of Eigenfunctions Of One Discontinuous Spectral Problem For Second Order Differential Equation For Grand-Lebesgue Space, Yusuf Zeren, Miqdad Ismailov, Fati̇h Şi̇ri̇n
On Basicity Of The System Of Eigenfunctions Of One Discontinuous Spectral Problem For Second Order Differential Equation For Grand-Lebesgue Space, Yusuf Zeren, Miqdad Ismailov, Fati̇h Şi̇ri̇n
Turkish Journal of Mathematics
Basicity of the system of eigenfunctions of some\textbf{ }discontinuous spectral problem for a second order differential equation with spectral parameter in boundary condition for grand-Lebesgue space $L_{p)} (-1;1)$ is studied in this work. Since the space is nonseparable, a subspace suitable for the spectral problem is defined. The subspace $G_{p)} (-1;1)$ of $L_{p)} (-1;1)$ generated by shift operator is considered. Basicity of the system of eigenfunctions for the space $G_{p)} (-1;1)\oplus C$, $1