Generalized derivatives and integrals of the Cezaro-Perron type. I} / A. V. Dergachev. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 2. P. 14-25 [Moscow Univ. Math. Bulletin. Vol. 69, N 2, 2014.].
Several equivalent definitions of Cesaro Ck-derivative and CkP-integral are shown to behave better than the original definition by Burkill in certain cases. For instance, a certain descriptive characterisation of Cesaro-Perron major and minor functions is obtained, and relations between Cesaro upper and lower derivatives and approximate derivatives of a function are established.
Key words: Cesaro derivatives, Cesaro-Perron integral, approximate derivatives, VBG functions.