Relation Between $L_{p}$-Derivates and Peano, Approximate Peano and Borel Derivates of Higher Order

Abstract

The definition of the $L_{p}$-derivative is such that it involves only the absolute value of the function and therefore the definition of $L_{p}$-derivates is not possible from the definition of $L_{p}$-derivative. Therefore, a special technique is used to define them and relations between $L_{p}$-derivates and Peano, approximate Peano and Borel derivates are studied.