Generalization and Refinements of Hermite-Hadamard's Inequality

Abstract

In this article, with the help of the concept of the harmonic sequence of polynomials, the well known Hermite-Hadamard's inequality for convex functions is generalized to cases with bounded derivatives of nth order, including the so-called n-convex functions, from which Hermite-Hadamard's inequality is extended and refined.

Some Generalizations of Integral Inequalities of Hermite-Hadamard Type for n-Time Differentiable Functions

“…Now we are in a position to generalize the above six theorems recited from [5] to more general cases. [ , ] …”

“…The aim of this paper is to, by establishing two integral identities and Hölder integral inequality, generalize the above six theorems recited from [5] to more general cases.…”

“…For generalizing the above six theorems recited from [5] to more general cases, we need the following integral identities.…”

Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex

“…new inequalities of Hermite-Hadamard pe inequalities were created in, for example, [8][9][10][11][12][13][14][15][16][17], especially the monographs [18,19], and related references therein.…”

Some inequalities of Hermite--Hadamard type for functions whose second derivatives are boldsymbol (α,m )-convex

“…In recent years, some other kinds of Hermite-Hadamard type inequalities were generated in, for example, [4,7,8,10,11,12]. For more systematic information, please refer to monographs [3,6] and related references therein.…”