Generalizations of Hermite--Hadamard type inequalities for MT-convex functions

Abstract

In this paper, we discover two novel integral identities for twice differentiable functions. Under the utility of these identities, we establish some generalized inequalities for classical integrals and Riemann-Liouville fractional integrals of the Hermite-Hadamard type via functions whose derivatives absolute values are MTconvex. At the end, we present applications for special means and several error approximations for the trapezoidal formula.

Some new inequalities of Hermite-Hadamard type for s-convex functions with applications

“…The following identity for the twice differentiable function, which was discovered by Chu et al [51], will be used in the next section.…”

Hermite-Hadamard type fractional integral inequalities for generalized (s,m,\varphi)-preinvex functions

“…In recent years, various generalizations, extensions and variants of such inequalities have been obtained (see [20]- [22]). For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, (see [18]) and the references cited therein, also (see [9]- [17]) and the references cited therein.…”

Hermite-Hadamard type fractional integral inequalities for MT$_{(m,\varphi)}$-preinvex functions

“…For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, (see [13]) and the references cited therein, also (see [3], [4], [5], [8], [9], [10], [17], [20]) and the references cited therein.…”