Derivatives of Divided Differences

Let V be a finite set containing k points. f (V ) is divided difference of f at V. The m-th order Peano derivative of f ({x}V) is defined and is denoted by fm(x;V ). It is same as generalised divided diference which is defined in [1]. We have proved a decomposition theorem and a mean value theorem for this generalised divided diference. Also many of the properties are studied.