On the Theory of n-Polynomial ϕ-Convex Functions
Journal of Function Spaces, vol.2026, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2026 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1155/jofs/9176813
- Journal Name: Journal of Function Spaces
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Middle East & Africa Database (ProQuest), Natural Science Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: convex functions, Hermite-Hadamard Inequality, <italic>n</italic>-polynomial convex functions, <italic>phi</italic>-convex functions
- Ataturk University Affiliated: Yes
Abstract
This paper introduces a novel extension of n-polynomial convex functions, referred to as “n-polynomial ϕ-convex functions”. The proposed concept generalizes the existing notion of n-polynomial convexity introduced in the recent literature. Within this new structural framework, we derive several novel inequalities and show that the absolute derivative of a function can characterise this specific convexity class. Our results show that employing the Hölder– (Formula presented.) can and enhanced power-mean integral inequalities yields significantly sharper and more efficient bounds compared to those obtained via standard Hölder and power-mean approaches. Furthermore, we provide explicit examples, algorithmic simulations, and visual graphs to validate the theoretical attributes of the definition. The proposed framework is expected to contribute to the development of integral inequality theory and special functions.