Some Extended Trapezoid-Type Inequalities and Applications

Abstract

Abstract. In this paper, we shall establish some extended trapezoid-typeinequalities for di¤erentiable convex functions and di¤erentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Ostrowski formulae are also given.

On the refinements of some important inequalities via $(p,q)$-calculus and their applications

“…Based on the convexity of mappings, many mathematicians have established different classes of inequalities, such as the Hardy-type inequality [13], Ostrowski-type inequality [4], midpoint-type inequality [5], trapezoidal-type inequality [29], Simpson-type inequality [32], and so on, among which the most famous is the Hermite-Hadamard inequality…”