Infinite approximate Peano derivatives

Abstract

Abstract. In this paper we introduce approximate Peano derivatives with infinite values allowed, and we show that these derivatives are Baire one, and possess the Darboux and Denjoy-Clarkson properties. Also we show that if they are bounded from above or below on an interval, then the corresponding ordinary derivatives exist and equal the approximate Peano derivatives.

A generalization of the GGR conjecture

“…The Peano derivatives were invented by Peano in [31] and then developed by de la Vallée Poussin in [13]. More recent developments in this subject can be found in [16,17,19,21].…”