Generalized Kantorovich forms of exponential sampling series
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Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Basel Ag
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we introduce a new family of operators by generalizing Kantorovich type of exponential sampling series by replacing integral means over exponentially spaced intervals with its more general analogue, Mellin Gauss Weierstrass singular integrals. Pointwise convergence of the family of operators is presented and a quantitative form of the convergence using a logarithmic modulus of continuity is given. Moreover, considering locally regular functions, an asymptotic formula in the sense of Voronovskaja is obtained. By introducing a new modulus of continuity for functions belonging to logarithmic weighted space of functions, a rate of convergence is obtained. Some examples of kernels satisfying the obtained results are presented.
Açıklama
Anahtar Kelimeler
Exponential sampling series; Kantorovich operators; Gauss-Weierstrass kernel; Mellin differential operator; Pointwise convergence; Asymptotic formula
Kaynak
Analysis and Mathematical Physics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
12
Sayı
2
