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We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p , h) fractional type inequality and many others, as the (p , h) -convexity is the generalization of the other convex inequalities. As a consequence of the (h , m) -convexity, the fractional inequality of the (s , m) -type is obtained. Many consequences of such fractional inequalities and generalizations are obtained. [ABSTRACT FROM AUTHOR]

We establish various fractional convex inequalities of the Hermite–Hadamard type with addition to many other inequalities. Various types of such inequalities are obtained, such as (p,h) fractional type inequality and many others, as the (p,h)-convexity is the generalization of the other convex inequalities. As a consequence of the (h,m)-convexity, the fractional inequality of the (s,m)-type is obtained. Many consequences of such fractional inequalities and generalizations are obtained.

In this paper, we introduce a new class of (p, h)-convex functions which generalize P-functions and convex, h, p, s-convex, Godunova-Levin functions, and we give some properties of the functions. Moreover, we establish the corresponding Schur, Jensen, and Hadamard types of inequalities. [ABSTRACT FROM AUTHOR]