Some Hermite–Hadamard type inequalities for log-h-convex functions

Abstract

In the paper, the authors introduce a notion "log-h-convex functions" and establish several Hermite-Hadamard type integral inequalities for this kind of functions.

Hermite–Hadamard type inequalities for differentiable $${h_{\varphi}}$$ h φ -preinvex functions

“…reduces to the definition for h ϕ -convex functions (see [16]). (4) For ϕ = 0 and η(v, u) = v − u Definition 2.5 reduces to the definition for h-convex functions (see [24]).…”

“…She studied the basic properties of h-convex functions and noticed that along with classical convexity this class also generalizes several other classes of convex functions such as, s-convex functions [2], Q functions [6] and P functions [5] respectively. Noor et al [16] introduced another generalization of classical convexity which is called as h ϕ -convex functions. Several Hermite-Hadamard type inequalities are proved for h ϕ -convex functions.…”

Some inequalities of Hermite-Hadamard type for $r$-$\varphi$-preinvex functions

“…In [11,12,13], some Hermite-Hadamard type inequalities for preinvex and log-preinvex functions were established.…”

On Giaccardi's Inequality and Associated Functional in the Plane

“…Many authors consider this function e.g. see [12], in which some of the properties of log convex functions has been discussed (also see [6,7,9] and references therein). In the following defintion, we define log convex function on coordinates.…”