Abel–Gontscharoff boundary value problems on measure chains

We discuss the Abel–Gontscharoff boundary value problem on a measure chain in two aspects, namely, the existence and uniqueness of solutions, and the convergence of iterative methods which include quasilinearization, approximate quasilinearization, Picardʹs and approximate Picardʹs methods. Examples are also presented to dwell upon the importance of the results obtained.