Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Certain Inequalities for Convex Functions

This is a review paper on some new inequalities for convex functions of one and several variables. The most important result presented for convex functions of one variable is the extension of Jensen’s inequality to affine combinations. The most interesting results presented for convex functions of several variables refer to inequalities concerning simplexes and its cones. Mathematics subject cl...

Some Hermite-Hadamard-like Type Inequalities for Logarithmically Convex Functions

Inequalities of Ando's Type for $n$-convex Functions

By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.

Fejér Type Inequalities for Harmonically-convex Functions with Applications

In this paper, a new weighted identity involving harmonically symmetric functions and differentiable functions is established. By using the notion of harmonic symmetricity, harmonic convexity and some auxiliary results, some new Fejér type integral inequalities are presented. Applications to special means of positive real numbers are given as well.

Hermite-Hadamard Type Inequalities for MφA-Convex Functions

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...