Hermite-hadamard type inequalities for P-convex functions

One of the properties of convex functions is that they satisfy the Hermite-Hadamard inequality, which provides lower and upper bounds for the integral mean of the function in terms of its valuesat the integral limits of the function. Right and left Hermite-Hadamard type inequalities have been expressed in the literature for p-convex functions, which are generalizations of convex functions, and for functions whose absolute value is p-convex. In this work, these studies were compiled and Hermite-Hadamard type inequalities were obtained for functions whose absolute value of the second derivative is p-convex, which have not yet been found in the literature. In this way, it is aimed to bring together the Hermite-Hadamard type inequalities given for p-convex functions and to create a resource for those interested in the subject. In the study, the basic properties of p-convex functions, Hermite-Hadamard inequalities for functions whose absolute value and derivative are p-convex, and integral identities involving the second derivative are presented. Then, by using these integral identities, Hermite-Hadamard-type inequalities for functions whose second derivative's absolute value is p-convex are derived. In the obtained inequalities, an example of a p-convex function is provided, and inequalities related to certain special functions and averages are given as applications.