# Lp-error Bounds Of Two And Three-point Quadrature Rules For Riemann-stieltjes Integrals

## TL;DR

This paper derives Lp-error bounds for two and three-point quadrature rules applied to Riemann-Stieltjes integrals, using novel triangle inequalities to improve error estimation techniques.

## Contribution

It introduces new triangle inequalities for Riemann-Stieltjes integrals and applies them to establish Lp-error bounds for specific quadrature rules.

## Key findings

- Lp-error bounds for two-point quadrature rules
- Lp-error bounds for three-point quadrature rules
- New triangle inequalities for Riemann-Stieltjes integrals

## Abstract

In this work, Lp-error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are give n. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals