On separation by function of bounded variation

Abstract

AbstractIn the present paper we are concerned with the problem of separation of two given functions by an increasing (decreasing) function or by a function of bounded variation. In the context of separation by a function of bounded variation we give two approaches. The first one concerns the separation with respect to the classical order in the set of real numbers, and this allow us to the new concept of variation involving two functions. This approach in fact leads us to the unusual phenomenon, namely the bounded joint variation of two functions forces these functions to be essentially the same. The second approach concerns the separation with respect to the partial order generated by the Lorentz cone.