Generalized n-Polynomial p-Convexity and Related Inequalities
Mathematics, cilt.12, sa.7, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 12 Sayı: 7
- Basım Tarihi: 2024
- Doi Numarası: 10.3390/math12071042
- Dergi Adı: Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: convex function, n-polynomial convexity, generalized n-polynomial p-convexity, Hermite-Hadamard inequality, integral inequalities
- Kırklareli Üniversitesi Adresli: Evet
Özet
In this paper, we construct a new class of convex functions, so-called generalized n-polynomial p-convex functions. We investigate their algebraic properties and provide some relationships between these functions and other types of convex functions. We establish Hermite–Hadamard (H–H) inequality for the newly defined class of functions. Additionally, we derive refinements of H–H inequality for functions whose first derivatives in absolute value at certain power are generalized n-polynomial p-convex. When (Formula presented.), our definition evolves into a new definition for the class of convex functions so-called generalized n-polynomial harmonically convex functions. The results obtained in this study generalize regarding those found in the existing literature. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.