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On Flett's mean value theorem.
- Source :
- Aequationes Mathematicae; Aug2015, Vol. 89 Issue 4, p1133-1165, 33p
- Publication Year :
- 2015
-
Abstract
- The paper deals with the mean value theorem of differential and integral calculus due to Flett (Math Gazette 42:38-39, ) and its various extensions. Since this theorem is a source of interest in various fields of mathematics (including functional equations), we aim to provide a detailed study of various (known as well as new) sufficient conditions for its validity, their geometric interpretations, and a comparison of the corresponding classes of functions. Moreover, our approach enables many new alternative proofs of known results, for instance, Pawlikowska's extension of Flett's theorem for higher-order derivatives. Some interesting open problems are also formulated. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 89
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 103382866
- Full Text :
- https://doi.org/10.1007/s00010-014-0311-5