Gegenbauer Transformations Nikolski-Besov Spaces Generalized by Gegenbauer Operator and Their Approximation Characteristics
Yazarlar (1)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
| Makale Türü | Özgün Makale (Uluslararası alan indekslerindeki dergilerde yayınlanan tam makale) | ||
| Dergi Adı | |||
| Makale Dili | – | Basım Tarihi | 01-2017 |
| Makale Linki | https://www.researchgate.net/profile/Vagif-Guliyev/publication/318709377_Gegenbauer_Transformations_Nikolski-Besov_Spaces_Generalized_by_Gegenbauer_Operator_and_Their_Approximation_Characteristics/links/59c8e7eaa6fdccc71929c82c/Gegenbauer-Transformat | ||
| UAK Araştırma Alanları |
Matematiksel Analiz
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| Özet |
| In this paper we consider some problems of the theory of approximation of functions on interval [0,∞) in the metric of Lp, λ with weight sh2λ x using generalized Gegenbauer shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Gegenbauer shifts. We establish the equivalence of the modulus of smoothness and K-functional, defined in terms of the space of the Sobolev type corresponding to the Gegenbauer differential operator. We define function spaces of Nikol’skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use some functions classes of spectrum. In these classes, we prove analogues of Bernstein’s inequality and others for the Gegenbauer differential operator. Our results are analogues of the results for generalized Bessel shifts obtained in the work [30]. |
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