A GENERALIZATION OF THE PEANO KERNEL AND ITS APPLICATIONS

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Atıf İçin Kopyala

Budakçi G., Oruç H.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.67, sa.2, ss.229-241, 2018 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 67 Sayı: 2
• Basım Tarihi: 2018
• Doi Numarası: 10.1501/commua1_0000000877
• Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.229-241
• Anahtar Kelimeler: Quantum B-splines, Peano kernel, q-Taylor theorem, divided differences, quantum derivatives, quantum integrals, Q-BERNSTEIN POLYNOMIALS, BEZIER CURVES, Q-TAYLOR, SPLINES
• Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Based on the q-Taylor Theorem, we introduce a more general form of the Peano kernel (q-Peano) which is also applicable to non-differentiable functions. Then we show that quantum B-splines are the q-Peano kernels of divided differences. We also give applications to polynomial interpolation and construct examples in which classical remainder theory fails whereas q-Peano kernel works.