(VC)(n)-ALMOST PERIODIC FUNCTIONS
S. Stoiński · Demonstratio Mathematica · 1999
In this note we give the definition and some properties of (VC)^n^-almost periodic functions, i.e. uniformly almost periodic and almost periodic in variation functions with first n derivatives.Let us denote for an arbitrary t G R by V(t; /) the Jordan variation of a function / on the interval (t -1, t + 1).Let us put X^n ) = {/ : R-»R : / e C(t)| + V(t;fW)). te R jt=oWe say that / € is a (VC)™-bounded function if (VD) 0 there exists a 6 > 0 such that (VD)( n \f -f h ) < e for every h G R with \h\< 6, we say that / G xj n) is a (VC)^ -continuous function.