Some extended trapezoid-type inequalities and applications

Abstract

In this paper, we shall establish some extended trapezoid-type$$\bigg|\dfrac{c-a}{b-a}f(x)+\dfrac{b-c}{b-a}f(y)-\dfrac{1}{b-a}\int_a^bf(t)dt\bigg|,\:(a\leq x\leq c\leq y\leq b)$$inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Ostrowski formulae are also given.