Turkish Journal of Mathematics
Abstract
We prove that Gadjieva's conjecture holds true as stated in her PhD thesis. The positive solution of this conjecture allows us to obtain improved versions of the Jackson--Stechkin type inequalities obtained in her thesis and some others. As an application, an equivalence of the modulus of smoothness with the realization functional is established. We obtain a characterization class for the modulus of smoothness.
DOI
10.3906/mat-1707-69
Keywords
Modulus of smoothness, Muckenhoupt weight, weighted Lebesgue spaces, characterization, $K$-functional
First Page
1484
Last Page
1503
Recommended Citation
AKGÜN, RAMAZAN
(2018)
"Gadjieva's conjecture, $K$-functionals, and someapplications in weighted Lebesgue spaces,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 58.
https://doi.org/10.3906/mat-1707-69
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/58