Some Results on ω-Derivatives and BV-ω Functions

Abstract

Let ω(x) be non-decreasing on the closed interval [a, b]. Outside the interval ω(x) is defined by ω(x) = ω(a) for x < a and ω(x) = ω(b) for x > b. Let S denote the set of points of continuity of ω(x) and D denote the set of points of discontinuity of ω(x). R. L. Jeffery [5] has defined the class U, of functions f(x) as follows: