Some Approximation Results on a Class of Szász-Mirakjan-Kantorovich Operators Including Non-negative parameter α

Özger F., Aslan R., Ersoy M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, cilt.46, sa.6, ss.461-484, 2025 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 46 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1080/01630563.2025.2474161
  • Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.461-484
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Alternative proofs of theWeierstrass uniformapproximation theorem

have been provided by numerous mathematicians, including

renowned ones. Among them, there was Bernstein that used

a set of polynomials known as the Bernstein polynomials. Motivated

by the advancements in computational disciplines,we propose

a new type of Szász-Mirakjan-Kantorovich operators that

incorporate a shape parameter α. Certain shape-preserving properties,

such as monotonicity and convexity, are achieved by computing

the first and second order derivatives of the proposed

operators. Certain approximation properties, including the statistical

rate of convergence, are also obtained using a regular

summability matrix. Finally, theoretical results are supported by

illustrative graphics and numerical experiments using the Mathematica

computer program. The operators defined in this paper

may be used in computer and computational sciences, including

in robotic manipulator control.