trapezoid inequality

In this study, we first establish two new identities for multiplicative differentiable functions. Based on these identities, we derive the midpoint and trapezoid type inequalities. The acquired outcomes improve and refine upon Khan and Budak's findings. At the conclusion, some applications to special means are provided.

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (η1,η2)-convex.

In this article, we first establish weighted identities based on twice partially differentiable mappings. Moreover, utilizing this equality, we derive  the weighted Hermite-Hadamard type inequalities via co-ordinated convex mappings in a rectangle from the plane $\mathbb{R}^{2}$. More specifically, we establish new inequalities using the Holder and power-mean inequalities. In addition, we obtain new results with special choices.

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.