In this paper, we utilize a variant of the Grüss inequality to obtain some new perturbed trapezoid inequalities. We improve the error bound of the trapezoid rule in numerical integration in some recent known results. Also we give a new Iyengar’s type inequality involving a second order bounded derivative for the perturbed trapezoid inequality.

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

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

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 (...

X iv :m at h/ 03 05 37 4v 1 [ m at h. N A ] 2 7 M ay 2 00 3 A GENERALISED TRAPEZOID TYPE INEQUALITY FOR CONVEX FUNCTIONS S.S. DRAGOMIR Abstract. A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf’s and (HH)−divergence measur...

An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided.

A new generalized perturbed trapezoid type inequality is established by Peano kernel approach. Some related results are also given.

Trapezoid inequality estimates the difference of integral mean a function on finite interval [a, b] and arithmetic its values at endpoints b. Quantum calculus is based diference principle or without concept limits. Euler-Jackson q-difference operator q-integral are discretization ordinary derivatives integrals they can be generalized to shifted versions arbitrary domain b]. In this paper we dis...