On new types of convex functions and their properties

M. Emin Özdemir

Published 2024-07-23Version 1

In this study, Firstly, we will write two new convex functions for $-1<n-\alpha \leq 1\ $and two new lemmas. Then we will find the relevance of the two new lemmas to Caputo-left-sided derivatives under additional conditions and draw conclusions about them. Secondly,We will give examples that support it. In what follows, we will rewrite the Hermite Hadamard integral inequality based on this new definitions. Furthermore, we will write an elementary inequality valid for value $-1<n-\alpha \leq 1.$