A three point quadrature rule for functions of bounded variation and applications

A three point quadrature rule approximating the Riemann integral for a function of bounded variation ff by a linear combination with real coefficients of the values f(a),f(x)f(a),f(x) and f(b)f(b) with x∈[a,b]x∈[a,b] whose sum is equal to b−ab−a is given. Applications for special means inequalities and in establishing a priori error bounds for the approximation of selfadjoint operators in Hilbert spaces by spectral families are provided as well.