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Turkish Journal of Mathematics

Authors

RAMAZAN AKGÜN

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

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Mathematics Commons

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