- Turkish Journal of Mathematics
- Vol: 42 Issue: 3
- Gadjieva’s conjecture, K -functionals, and some applications in weighted Lebesgue spaces
Gadjieva’s conjecture, K -functionals, and some applications in weighted Lebesgue spaces
Authors : Ramazan Akgün
Pages : 1484-1503
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Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Modulus of smoothness, Muckenhoupt weight, weighted Lebesgue spaces, characterization, $K$-functional