Abstract
The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference42 articles.
1. Some new Hermite–Hadamard type integral inequalities for the s–convex functions and theirs applications;Özcan;J. Inequal. Appl.,2019
2. Convex Functions and Their Applications;Niculescu,2006
3. Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means
4. Some new inequalities of Hermite-Hadamard type for s-convex functions with applications
5. Étude sur les propriétés des fonctions entiéres en particulier d’une fonction considéréé par Riemann;Hadamard;J. Math. Pures. Appl.,1893