Refinements of the weighted generalized trapezoid inequality in terms of cumulative variation and applications

In this paper, we first establish some refinements of the weighted generalized trapezoid inequality for functions of bounded variation in terms of a cumulative variation function, and then obtain some perturbed versions of the weighted generalized trapezoid inequality. Several applications for selfadjoint operators on complex Hilbert spaces are also given.

Improvements of Ostrowski and generalised trapezoid inequality in terms of the upper and lower bounds of the first derivative

In this paper improvements of the Ostrowski and generalised Trapezoid inequalities are found in terms of the upper and lower bounds of the first derivative.

A quasi-trapezoid inequality for double integrals

A quasi-trapezoid inequality is derived for double integrals that strengthens considerably existing results. A consonant version of the Grüss inequality is also derived. Applications are made to cubature formulæ and the error variance of a stationary variogram.

On trapezoid inequality via Gruss type result and applications

In this paper, we point out a Gr"uss type inequality and apply it for special means (logarithmic mean, identric mean etc ...) and in Numerical analysis in connection with the classical trapezoid formula.