A GENERALIZATION OF THE PEANO KERNEL AND ITS APPLICATIONS
COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.67, sa.2, ss.229-241, 2018 (ESCI, TRDizin)
- 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
- 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.