Novel Fractional Simpson–Mercer-Type Inequalities and Their Applications
Journal of Mathematics, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2026 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1155/jom/7179835
- Dergi Adı: Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: convex function, Lipschitz function, Riemann–Liouville fractional integrals, Simpson–Mercer-type inequalities, simulation
- Kocaeli Üniversitesi Adresli: Evet
Özet
In this paper, we establish a Mercer-type identity for the Riemann–Liouville fractional integral. By using this identity, we derive several fractional Simpson–Mercer-type inequalities for functions whose third derivatives satisfy convexity-type assumptions in absolute value. Related estimates are also obtained under boundedness and Lipschitz continuity assumptions on the third derivative. Several known Simpson-type inequalities are recovered as special cases of the main results. To illustrate the effectiveness of the proposed results, numerical examples are provided. Furthermore, applications to Simpson-type quadrature formulas and the q-digamma function are discussed.