Ramazan AKGÜN

7792

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

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,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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