Generalized derivatives and integrals of Cesàro–Perron. Type. I
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2014), pp. 14-25
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Several equivalent definitions of Cesàro $C_k$-derivative and $C_kP$-integral are shown to behave better than the original definition by Burkill in certain cases. For instance, a certain descriptive characterisation of Cesàro–Perron major and minor functions is obtained, and relations between Cesàro upper and lower derivatives and approximate derivatives of a function are established.
@article{VMUMM_2014_2_a2,
author = {A. V. Dergachev},
title = {Generalized derivatives and integrals of {Ces\`aro{\textendash}Perron.} {Type.~I}},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {14--25},
year = {2014},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2014_2_a2/}
}
A. V. Dergachev. Generalized derivatives and integrals of Cesàro–Perron. Type. I. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2014), pp. 14-25. http://geodesic.mathdoc.fr/item/VMUMM_2014_2_a2/
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