INEQUALITIES PERTAINING TO GENERAL FRACTIONAL INTEGRAL OPERATORS FOR S-CONVEX FUNCTIONS IN THE THIRD SENSE
Advanced Mathematical Models and Applications, vol.11, no.2, pp.414-427, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: 2
- Publication Date: 2026
- Doi Number: 10.62476/amma112414
- Journal Name: Advanced Mathematical Models and Applications
- Journal Indexes: Scopus
- Page Numbers: pp.414-427
- Keywords: Generalized Fractional Integral, Hermite-Hadamard Type Inequality, s-convexity in the Third Sense
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
This article investigates a novel class of inequalities for s-convex functions in the third sense, utilizing generalized fractional integral operators with respect to another function. We establish two foundational theorems that characterize both left-sided and right-sided fractional integral operators, providing a comprehensive framework for this specific function class. Building upon these core results, we derive a series of theorems that elucidate the intricate relationships between the proposed inequalities. To demonstrate the versatility and scope of our findings, we specialize the results to Riemann-Liouville and Hadamard fractional integral settings. Notably, the theoretical framework is applied to yield significant new inequality relations among key special functions, including Beta and Incomplete Beta functions, Gamma and Incomplete Gamma functions, and Imaginary Error functions, thereby bridging abstract fractional calculus with practical analytic applications. Furthermore, it is demonstrated that one of these inequalities provide significantly sharper bounds than analogue one currently established in the literature.