Abstract In this paper, we obtain new Hermite–Hadamard-type inequalities for r -convex and geometrically convex functions and, additionally, some by using the Hölder–İşcan integral inequality an improved power-mean inequality.

The main target of this paper is to discuss operator Hermite–Hadamard inequality for convex functions, without appealing convexity. Several forms will be presented and some applications including norm mean inequalities shown too.

In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We the q?2-quantum integral show midpoint trapezoidal q?2-differentiable functions. Furthermore, an example that previously proved Hermite–Hadamard-type inequality via q?1-quantum is not valid functions, present its proper form. q?1-...

Recently, Hermite-Hadamard-type inequalities and their applications have attracted considerable interest, as shown in the book [1], for example. These inequalities have been studied for various classes of functions such as convex functions [1], quasiconvex functions [2–4], p-functions [3, 5], Godnova-Levin type functions [5], r-convex functions [6], increasing convex-along-rays functions [7], a...

In this study, firstly, Hermite-Hadamard type inequalities are examined for functions whose first derivative is $s$-convex in the fourth sense. addition, second Finally, some application examples including special tools and digamma presented.

holds. This double inequality is known in the literature as Hermite-Hadamard integral inequality for convex functions. Note that some of the classical inequalities for means can be derived from (1.1) for appropriate particular selections of the mapping f . Both inequalities hold in the reversed direction if f is concave. For some results which generalize, improve and extend the inequalities (1....

Abstract In this study, we introduce the new concept of $$h$$ h -convex fuzzy-interval-valued functions. Under concept, present versions Hermite–Hadamard inequalities (H–H inequalities) are called fuzzy-interval type for functions ( FIVF) by means fuzzy order relation. This relation is defined level wise thro...

A new generalization of the Katugampola generalized fractional integrals in terms Mittag-Leffler functions is proposed. Consequently, generalizations Hermite-Hadamard inequalities by this newly proposed integral operator, for a positive convex stochastic process, are established. Other known results easily deduced as particular cases these inequalities. The obtained also hold any function.