A refinement of Ostrowski's inequality for absolutely continuous functions and applications (Q1873627)

A refined version of an Ostrowski type inequality for absolutely continuous functions is derived. The bounds involve \(L_1\) norms of the derivative of the function under consideration, taken over appropriate subsets of the interval in question. Applications yield inequalities involving certain means (arithmetic, logarithmic, geometric, identric, etc.), error estimates for certain simple quadrature formulas, bounds for probability distribution functions, and Jeffrey's distance measure in information theory.