Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 315-320

TOPOLOGICAL GENERALIZATION OF CAUCHY'S MEAN VALUE THEOREM

Ivan Kupka

Comenius University, Faculty of Mathematics, Physics and Informatics
Department of Mathematical Analysis and Numerical Mathematics
Mlynska Dolina, Bratislava, Slovakia; ivan.kupka 'at' seznam.cz

Abstract. The main goal of the paper is to introduce and study the relative derivatives for general topological spaces. We also prove a generalization of Rolle's and Cauchy's mean value theorems for real valued functions defined on topological spaces.

2010 Mathematics Subject Classification: Primary 54C30, 26A24; Secondary 26A06, 26A99.

Key words: Generalized derivatives, Cauchy's mean value theorem.

Reference to this article: I. Kupka: Topological generalization of Cauchy's mean value theorem. Ann. Acad. Sci. Fenn. Math. 41 (2016), 315-320.

Full document as PDF file

doi:10.5186/aasfm.2016.4120