Gadjieva's conjecture, K -functionals, and some applications in weighted Lebesgue spaces | Zendy

Ramazan Akgün | Zendy

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Gadjieva's conjecture, K -functionals, and some applications in weighted Lebesgue spaces

Author(s) -

Ramazan Akgün

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1707-69

Subject(s) - mathematics , conjecture , smoothness , characterization (materials science) , pure mathematics , equivalence (formal languages) , realization (probability) , collatz conjecture , discrete mathematics , class (philosophy) , combinatorics , mathematical analysis , computer science , statistics , materials science , artificial intelligence , nanotechnology

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.

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