Optimal Abel–Gontscharoff interpolation error bounds on measure chains

In this paper we offer the best possible error bounds for Abel–Gontscharoff interpolation on a measure chain. Our results unify the error analysis performed on continuous and discrete Abel–Gontscharoff interpolation. Furthermore, as an application of the error estimates obtained, criteria are developed for the right disfocality as well as disconjugacy for a higher order equation on a measure chain.