Jensen inequality for strongly h-convex functions and a characterization of pairs of functions that can be separated by a strongly h-convex function are presented. As a consequence, a stability result of the Hyers-Ulam type is obtained.
In this paper, firstly we prove an integral identity that one can derive
several new equalities for special selections of n from this identity:
Secondly, we established more general integral inequalities for functions
whose second derivatives of absolute values are GA-convex functions based
on this equality.
In this paper, we give a new concept which is a generalization of the
concepts quasi-convexity and harmonically quasi-convexity and establish a
new identity. A consequence of the identity is that we obtain some new
general inequalities containing all of the Hermite-Hadamard and Simpson-like
type for functions whose derivatives in absolute value at certain power are
p-quasi-convex. Some applications to special means of real numbers are also
given.
Strong h-Convexity and Separation Theorems