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

Quasi Grüss type inequalities for complex functions defined on unit circle with applications for unitary operators in Hilbert spaces

Some quasi Grüss type inequalities for the Riemann-Stieltjes integral of continuous complex valued integrands defined on the complex unit circle C (0; 1) and various subclasses of integrators are given. Natural applications for functions of unitary operators in Hilbert spaces are provided.peerReviewe

Ostrowski and Trapezoid Type Inequalities for the Stieltjes Integral with Lipschitzian Integrands or Integrators

Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lischitzian integrators for both Hölder continuous and monotoonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well