Simpson, midpoint, and trapezoid-type inequalities for multiplicatively s-convex functions
Demonstratio Mathematica, cilt.58, sa.1, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 58 Sayı: 1
- Basım Tarihi: 2025
- Doi Numarası: 10.1515/dema-2024-0060
- Dergi Adı: Demonstratio Mathematica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Linguistic Bibliography, MathSciNet, zbMATH, Directory of Open Access Journals
- Anahtar Kelimeler: multiplicative calculus, multiplicatively <italic>s</italic>-convex function, Simpson inequality, midpoint-type inequality, trapezoid-type inequality
- Kırklareli Üniversitesi Adresli: Evet
Özet
In this study, we establish new generalizations and results for Simpson, midpoint, and trapezoid-type integral inequalities within the framework of multiplicative calculus. We begin by proving a new identity for multiplicatively differentiable functions. Using this identity, we then obtain a new Simpson-type inequality for multiplicatively s s -convex functions. Additionally, we derive novel integral inequalities related to the right and left sides of the Hermite-Hadamard inequality for multiplicatively s s -convex functions. We also demonstrate that some of the results obtained here improve upon known results, while others are generalizations. Finally, we present some applications to special means.