A sharp companion of Ostrowski's inequality for the Riemann–Stieltjes integral and applications

Mohammad W. Alomari
2016 Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica  
A sharp companion of Ostrowski's inequality for the Riemann-Stieltjes integral $\int_a^b {f(t)\;du(t)} $ , where f is assumed to be of r-H-Hölder type on [a, b] and u is of bounded variation on [a, b], is proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.
doi:10.1515/aupcsm-2016-0006 fatcat:g4haapm36fbwrbtzagvzqaymr4