Generalization of the classical derivative and analogue of the differentiation operator as a toolset for studying the differential properties of functions

• Date: 2020
• Author Affiliations: R.Yu. Osaulenko — National Technical University of Ukraine "Kyiv Polytechnic Institute named after Igor Sikorsky"
• Keywords: keywords
• Main Authors: Osaulenko, R.Yu., Осауленко, Р.Ю.
• Format: Article
• Language: Ukrainian; English
• Published: Інститут математики НАН України 2020
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/399
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

In this paper, we consider a $(u, w)$--derivative that is a generalization of a classical derivative and an operator defined by the equality $Sqxuv f (x) = \lim\limits_{h \rightarrow 0}\frac{Squv f(x)}{Squv x}$, where $Squv f(x)$ is the oscillation of the function $ f $ on the interval with the ends...