CONSTRUCTION OF A NEW CLASS OF FUNCTIONS WITH THEIR SOME PROPERTIES AND CERTAIN INEQUALITIES: n-FRACTIONAL POLYNOMIAL CONVEX FUNCTIONS
Miskolc Mathematical Notes, vol.24, no.3, pp.1389-1404, 2023 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 24 Issue: 3
- Publication Date: 2023
- Doi Number: 10.18514/mmn.2023.4142
- Journal Name: Miskolc Mathematical Notes
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
- Page Numbers: pp.1389-1404
- Keywords: convex function, Hermite-Hadamard inequality, Hölder integral inequality, Hölder-İşcan integral inequality, n-fractional polynomial convexity
- Open Archive Collection: AVESIS Open Access Collection
- Karadeniz Technical University Affiliated: No
Abstract
In this paper, we introduce a new function class called n-fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n-fractional polynomial convex. Also, we compare the results obtained with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given.