Error Bounds of Boole’s Formula for Twice Differentiable Convex Functions with Numerical Analysis
Latin American Journal of Mathematics, cilt.5, sa.1, ss.88-104, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 5 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.14244/lajm.v5i1.106
- Dergi Adı: Latin American Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.88-104
- Anahtar Kelimeler: error bound, Inequalities of Boole’s rule, twice differentiable convex function
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Kocaeli Üniversitesi Adresli: Evet
Özet
This study investigates the error bounds associated with Boole’s formula, a well-known open Newton–Cotes technique. By focusing on twice differentiable functions, a novel identity for Boole’s formula is established. Establishing a new identity is a challenging task in this research because suitable kernels need to be found by replacing unknown values. The number of equations is greater than the number of unknowns, so the system has infinitely many solutions, and only one is suitable for Boole’s type identity. Using the newly established equality, several Boole’s type inequalities for twice differentiable convex functions are demonstrated. It offers significant advancements in the domain of computational mathematics and its applications. Additionally, numerical examples and graphical illustrations are included to validate the significance and applicability of these newly established inequalities.