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.
The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.
AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.
Weighted version of Hermite–Hadamard type inequalities for geometrically quasi-convex functions and their applications
