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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We obtain a characterization class for the modulus of smoothness.
📌 3 Key Takeaways
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Objective & Hypothesis:We prove that Gadjieva's conjecture holds true as stated in her PhD thesis.
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Key Findings & Data: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.
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Conclusion & Impact:We obtain a characterization class for the modulus of smoothness.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Modulus of smoothness · Muckenhoupt weight · weighted Lebesgue spaces
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.
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Cite This Article
AKGÜN, R. (2022). Gadjieva’s conjecture, K -functionals, and some applications in weighted Lebesgue spaces. Turkish Journal of Mathematics, Cilt: 42 - Sayı: 3, 1484–1503. https://ajindex.com/articles/607839