Riemann–Liouville-type fractional generalization of Bernstein–Kantorovich operators
Lithuanian Mathematical Journal, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s10986-026-09731-4
- Dergi Adı: Lithuanian Mathematical Journal
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: computer graphics, fractional calculus, modulus of continuity, order of convergence, shape parameter α
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
Approximation theory is a substantial field of mathematical analysis that emerged in the 19th century and has been developed by mathematicians across the globe ever since. Its importance has increased over time, as it provides solutions to numerous scientific challenges not only in mathematics but also in fields like physics, engineering, etc. In the present work, we construct a Riemann–Liouville fractional-type generalization of Bernstein–Kantorovich operators. Firstly, we obtain some needed moment estimates. Also, we study some direct and local approximation properties of the constructed operators. Next, we serve up certain graphical and numerical results to demonstrate convergence, accuracy, and advantages of the constructed operators. Further, we provide bivariate type of the newly constructed operators and establish the degree of approximation through of partial and complete modulus of continuity. Lastly, we present some graphical representations and maximum error of approximation tables to verify the convergence behavior of bivariate extension of proposed operators.