Enhanced approximation techniques: Stancu-type (λ, μ)-Bernstein-Kantorovich operators
Applied Mathematics, cilt.41, sa.3, ss.742-762, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 41 Sayı: 3
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s11766-026-5536-2
- Dergi Adı: Applied Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Sayfa Sayıları: ss.742-762
- Anahtar Kelimeler: 41A10, 41A25, 41A36, A-statistical convergence, generalized λ-Bernstein operators, pointwise estimates, Stancu-type Bernstein-Kantorovich operators, Voronovskaya type theorem
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
The principal aim of this study is to investigate a range of approximation characteristics exhibited by Stancu-type generalized λ-Bernstein-Kantorovich operators denoted as Fr,α,βλ,μ(ϕ; z). In the initial stage, we conduct a comprehensive examination of diverse moment estimates pertaining to operators Fr,α,βλ,μ(ϕ; z). Subsequently, we delve into the exploration of several facets of direct results, including the order of convergence with respect to the usual modulus of continuity, Lipschitz-type continuous functions, and the Peetre’s K-functional. Furthermore, in order to gain insights into the asymptotic characteristics of the operators Fr,α,βλ,μ(ϕ; z), we derive a Voronovskaya-type asymptotic theorem. Additionally, we provide an analysis of the A-statistical convergence behavior and pointwise estimates associated with the operators Fr,α,βλ,μ(ϕ; z). Finally, we have included graphical representations and numerical error value tables to demonstrate the efficiency and accuracy of our proposed operator. Our analysis reveals that our operator yields significantly superior approximation results compared to certain other linear positive operators documented in the existing literature.