In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations...

Abstract In this article we give two possible generalizations of the Hermite–Hadamard integral inequality for class twice differentiable functions, where convexity property target function is not assumed in advance. They represent a refinement case convex/concave functions with numerous applications.

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.

Abstract In this paper, we present the Sugeno integral of Hermite–Hadamard inequality for case quasi-arithmetically convex (q-ac) functions which acts as a generator all quasi-arithmetic means in frame work integral.

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

In this paper, we present a weighted version of the Hermite–Hadamard inequality for convex functions on time scales, with weights that are allowed to take some negative values, these are the Steffensen–Popoviciu and the Hermite–Hadamard weights. We also present some applications of this inequality.

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.

In this paper, we establish several weighted inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works. Mathematics Subject Classification (2010): 26D15.

In this work, we address and explore the concept of generalized \(m\)-preinvex functions on fractal sets along with linked local fractional integral inequalities. Additionally, some engrossing algebraic properties are presented to facilitate current initiated idea. Furthermore, prove latest variant Hermite-Hadamard type inequality employing proposed definition preinvexity. We also derive severa...