On a functional equation related to a generalization of Flett's mean value theorem.
A function F is said to have a generalized Peano derivative at x if F is continuous in a neighborhood of x and if there exists a positive integer q such that a qth primitive of F in the neighborhood has the (q+n)th Peano derivative at x; in this case the latter is called the generalized nth Peano derivative of F at x and denoted by . We show that generalized Peano derivatives belong to the class [Δ’]. Also we show that they are path derivatives with a nonporous system of paths satisfying the I.I.C....
We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.