A new representation and shape-preserving properties of perturbed Bernstein operators

Acu A., MUTLU G., ÇEKİM B., YAZICI S.

Mathematical Methods in the Applied Sciences, cilt.47, sa.1, ss.5-14, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1002/mma.9636
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.5-14
  • Anahtar Kelimeler: Bernstein operators, computer graphics, computer-aided design, shape-preserving properties
  • Gazi Üniversitesi Adresli: Evet

Özet

We introduce a new representation of recently introduced perturbed Bernstein operators (Formula presented.) in terms of classical Bernstein operators. Using this new representation, we investigate the shape-preserving properties of the operator (Formula presented.). In particular, we prove that perturbed Bernstein operators preserve monotonicity and convexity of functions for certain cases. On the other hand, we demonstrate with some counterexamples that monotonicity and convexity preserving properties fail in other cases. Moreover, we present some weaker results in these cases.