No abstract

We establish a Fejér type inequality for harmonically convex functions. Our results are the generalizations of some known results. Moreover, some properties of the mappings in connection with Hermite-Hadamard and Fejér type inequalities for harmonically convex functions are also considered.

No abstract

No abstract

In this paper, we establish some new Hermite-Hadamard inequalities for s-convex functions via fractional integrals. Some Hermite-Hadamard type inequalities for products of two convex and s-convex functions via Riemann-Liouville integrals are also established.

In this paper, we generalize and sharpen the power means inequality by using the theory of majorization and the analytic techniques. Our results unify some optimal versions of the power means inequality. As application, a well-known conjectured inequality proposed by Janous et al. is proven. Furthermore, these results are used for studying a class of geometric inequalities for simplex, from which, some interesting inequalities including the refined Euler inequality and the reversed FinslerHadwiger type inequality are obtained.  2005 Elsevier Inc. All rights reserved.

The aim of this paper is to introduce a new extension of convexity called σ -convexity. We show that the class of σ -convex functions includes several other classes of convex functions. Some new integral inequalities of Hermite-Hadamard type are established to illustrate the applications of σ -convex functions. MSC: 26D15; 26D10; 26B25

In this work, we discover a new version of Hermite–Hadamard quantum integrals inequality via m-preinvex functions. Moreover, the authors present a quantum integrals identity and drive some new quantum integrals of Hermite–Hadamard-type inequalities involving generalized ( s , m ) -preinvex functions.