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

APPROXIMATING THE STIELTJES INTEGRAL VIA A WEIGHTED TRAPEZOIDAL RULE WITH APPLICATIONS

Abstract. In this paper we provide sharp error bounds in approximating the weighted Riemann-Stieltjes integral Applications for continuous functions of selfadjoint operators in complex Hilbert spaces are given as well

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

Some new generalized 2D Ostrowski-Grüss type inequalities on time scales

AbstractIn this paper, we present some new generalized 2D Ostrowski-Grüss type integral inequalities on time scales, which on one hand extend some known results in the literature, and on the other hand unify corresponding continuous and discrete analysis. New bounds for the 2D Ostrowski-Grüss type inequalities are derived, some of which are sharp