The Picard and Gauss-Weierstrass Singular Integrals in (p, q)-Calculus
Yükleniyor...
Tarih
2020
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
MALAYSIAN MATHEMATICAL SCIENCES SOC
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The vast development of the techniques in both the quantum calculus and the post-quantum calculus leads to a significant increase in activities in approximation theory due to applications in computational science and engineering. Herein, we introduce (p, q)-Picard and (p, q)-Gauss-Weierstrass integral operators in terms of the (p, q)-Gamma integral. We give a general formula for the monomials under both (p, q)-Picard and (p, q)-Gauss-Weierstrass operators as well as some special cases. We discuss the uniform convergence properties of them. We show that both operators have optimal global smoothness preservation property via usual modulus of continuity. Finally, we establish the rate of approximation using the weighted modulus of smoothness. Depending on the choices of parameters p and q in the integrals, we are able to obtain better error estimation than classical ones.
Açıklama
ARAL, Ali/0000-0002-2024-8607; Erbay, Hasan/0000-0002-7555-541X
Anahtar Kelimeler
(p, q)-Picard integral operator, (p, q)-Gauss-Weierstrass integral operator, Uniform convergence, Global smoothness
Kaynak
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
43
Sayı
2
Künye
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