No ultimate Peano derivative, but Laplace \dots ? (Q1978838)

This paper is an abstract of the lecture at Chattanooga Symposium. It deals with generalizations of Peano derivative -- generalized Peano derivative, ultimate Peano derivative and Laplace derivative. The ultimate Peano derivative is a generalization of the generalized Peano derivative and the Laplace derivative is a generalization of the ultimate Peano derivative. But there is no function having an ultimate Peano derivative at a fixed point but no generalized Peano derivative there. On the other hand there is a function having a Laplace derivative at a fixed point but no generalized Peano derivative there. The authors show that Laplace derivatives are Darboux Baire 1 functions, have the dense open set property and have the Denjoy property.