Generalized derivatives and integrals of Cesàro–Perron. Type. I

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.