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-...

In the paper, with help of two known integral identities and by virtue classical Hölder inequality, authors establish several new inequalities Hermite–Hadamard type for convex functions. These newly established generalize some results.

In this paper, using the definition of functions (h,m,s)-convex modified second type, various extensions classic Hermite-Hadamard Inequality are obtained Katugampola integrals. addition, we show that several results known particular cases ours.

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 shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

In this paper, the Hermite-Hadamard inequality for $p-$convex function is provided. Some integral inequalities them are also presented. Also, based on and double of sets, new functions defined under certain conditions, $p-$convexity these shown. expressed.

The principal motivation of this paper is to establish a new integral equality related k-Riemann Liouville fractional operator. Employing equality, we present several inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard inequality. Additionally, some novel cases the established results different kinds derived. This sums up Riemann–Liouville and Hermit...