Functions of Waterman-Shiba Bounded Variation with Variable Exponent

J. Gim´enez, O. Mej´ı

Abstract

In this paper we introduce the notion of functions of bounded variation in the Waterman-Shiba’s sense with variable exponent on a real interval [a, b] and we study some of its basic properties. We show that the set of all such functions generalize some known Banach spaces. Finally we exhibit a rich subclass of composite functions that belong to the introduced class