Further Properties of Quantum Spline Spaces

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Budakçı G., Oruç H.

MATHEMATICS, vol.8, no.10, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 10
  • Publication Date: 2020
  • Doi Number: 10.3390/math8101770
  • Journal Name: MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: quantum splines, q-B-splines, divided differences, q-derivatives, q-integrals
  • Dokuz Eylül University Affiliated: Yes

Abstract

We construct q-B-splines using a new form of truncated power functions. We give basic properties to show that q-B-splines form a basis for quantum spline spaces. On the other hand, we derive algorithmic formulas for 1/q-integration and 1/q-differentiation for q-spline functions. Moreover, we show a way to find the polynomial pieces on each interval of a q-spline function.