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, vol.47, no.1, pp.5-14, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.9636
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: 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
  • Page Numbers: pp.5-14
  • Keywords: Bernstein operators, computer graphics, computer-aided design, shape-preserving properties
  • Gazi University Affiliated: Yes

Abstract

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.