Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Path derivatives: a unified view of certain generalized derivatives


Authors: A. M. Bruckner, R. J. O’Malley and B. S. Thomson
Journal: Trans. Amer. Math. Soc. 283 (1984), 97-125
MSC: Primary 26A24
MathSciNet review: 735410
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A collection $ E = \{ {E_x}:x \in R\} $ is a system of paths if each set $ {E_x}$ has $ x$ as a point of accumulation. For such a system $ E$ the derivative $ F_E'(x)$ of a function $ F$ at a point $ x$ is just the usual derivative at $ x$ relative to the set $ {E_x}$. The goal of this paper is the investigation of properties that $ F$ and its derivative $ F_E'$ must have under certain natural assumptions about the collection $ E$. In particular, it is shown that most of the familiar properties of approximate derivatives and approximately differentiable functions follow in this setting from three conditions on the collection $ E$ relating to the "thickness" of the sets $ {E_x}$ and the way in which the sets intersect.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 26A24

Retrieve articles in all journals with MSC: 26A24


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0735410-1
PII: S 0002-9947(1984)0735410-1
Keywords: Derivatives, approximate derivatives, Peano derivatives, functions of Baire class $ 1$, Darboux functions
Article copyright: © Copyright 1984 American Mathematical Society