On functions of bounded kth variation

Abstract

Russell introduced the concept of functions of bounded  kth variation  (BVk  functions) and obtained  some properties. Das and Lahiri gave the definition of functions of related absolute continuity  (ACk  functions) and proved interrelations between  AC k  and  BVk  functions. In this paper the authors  consider the concept of  BVk  and  ACk  functions on a bounded set  E  dense in itself and prove that  these functions admit extensions to  BVk  ACk  functions on an interval [a, b] containing the  closure of the set  E.