- Turkish Journal of Mathematics
- Vol: 44 Issue: 3
- Korovkin-type theorems and their statistical versions in grand Lebesgue spaces
Korovkin-type theorems and their statistical versions in grand Lebesgue spaces
Authors : Yusuf Zeren, Mıqdad Ismailov, Cemil Karaçam
Pages : 1027-1041
Doi:10.3906/mat-2003-21
View : 11 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :The analogs of Korovkin theorems in grand-Lebesgue spaces are proved. The subspace G p −π; π 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 −π; π . The analogs of Korovkin theorems are proved in G p −π; π . These results are established in G p −π; π 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.Keywords : Grand Lebesgue space, Korovkin theorems, shift operator, statistical convergence, positive linear operator, approximation process