Mercer–Trapezoid Rule for the Riemann–Stieltjes Integral with Applications

In this paper several new error bounds for the Mercer - Trapezoid quadrature rule for the Riemann-Stieltjes integral under various assumptions are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well

A companion of Dragomir’s generalization of the Ostrowski inequality and applications to numerical integration

Some analogs of Dragomir’s generalization of the Ostrowski integral inequality are established. Some sharp inequalities are proved. An application to the composite quadrature rule is provided.Встановлено аналоги узагальнення Драгомiра iнтегральної нерiвностi Островського, отримано деякi точнi нерiвностi. Наведено застосування до складеної квадратурної формули

A NEW COMPANION OF OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS OF TWO VARIABLES WITH BOUNDED VARIATION

In this paper, we first define some functional which are obtained using Riemann-Stieltjes integral. Then, we establish a new companion of Ostrowski type inequalities for functions of two independent variables with bounded variation and give a numerical quadrature formula for the Riemann-Stieltjes integral