A generalization of the Schwarzian derivative and its applications

A generalization of the Schwarzian derivative is proposed; this generalization is used to investigate functions having divided differences which are nonzero in a given region. A relation is established between this class of functions and linear homogeneous differential equations.Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 229–238, August, 1971.