The Picard and Gauss–Weierstrass Singular Integrals in (p, q)-Calculus
| العنوان: | The Picard and Gauss–Weierstrass Singular Integrals in (p, q)-Calculus |
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| المؤلفون: | Hasan Erbay, Emre Deniz, Ali Aral |
| المساهمون: | KKÜ, Kırıkkale Üniversitesi |
| المصدر: | Bulletin of the Malaysian Mathematical Sciences Society. 43:1569-1583 |
| بيانات النشر: | Springer Science and Business Media LLC, 2019. |
| سنة النشر: | 2019 |
| مصطلحات موضوعية: | Approximation theory, Monomial, Smoothness (probability theory), General Mathematics, Uniform convergence, 010102 general mathematics, Gauss, q)-Picard integral operator, Singular integral, Quantum calculus, 01 natural sciences, Modulus of continuity, 010101 applied mathematics, q)-Gauss-Weierstrass integral operator, (p, Calculus, Global smoothness, 0101 mathematics, Mathematics |
| الوصف: | ARAL, Ali/0000-0002-2024-8607; Erbay, Hasan/0000-0002-7555-541X WOS:000526029300033 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. |
| وصف الملف: | application/pdf |
| تدمد: | 2180-4206 0126-6705 |
| DOI: | 10.1007/s40840-019-00759-z |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fb4012ce10e77fb8b1c6934dd672f89 https://doi.org/10.1007/s40840-019-00759-z |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi.dedup.....2fb4012ce10e77fb8b1c6934dd672f89 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 21804206 01266705 |
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| DOI: | 10.1007/s40840-019-00759-z |