Abstract
The main objective of this thesis is to find some characteristic properties of D.C. functions and deduce these properties by applying convex functions and functions of bounded variation. We shall state and prove some basic properties of both convex functions and functions of bounded variation. This paper is concerned with relationship among three notions: the convex functions, functions of bounded variation and differences of convex functions. Our main result is that, if f is differentiable on (a,b) and continuous on [a,b] and if {displaystyle underset{Pinmathcal{P}[a,b]}{sup}sumleft| riangle_{i+1}f- riangle_{i}f ight|<+infty}, then f is a D.C. function.
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