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Proceedings of the American Mathematical Society

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Infinite approximate Peano derivatives


Author: Hajrudin Fejzic
Journal: Proc. Amer. Math. Soc. 131 (2003), 2527-2536
MSC (2000): Primary 26A24; Secondary 26A21
DOI: https://doi.org/10.1090/S0002-9939-02-06828-4
Published electronically: October 15, 2002
MathSciNet review: 1974651
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Abstract: In this paper we introduce approximate Peano derivatives with infinite values allowed, and we show that these derivatives are Baire one, and possess the Darboux and Denjoy-Clarkson properties. Also we show that if they are bounded from above or below on an interval, then the corresponding ordinary derivatives exist and equal the approximate Peano derivatives.


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Additional Information

Hajrudin Fejzic
Affiliation: Department of Mathematics, California State University, San Bernardino, California 92407
Email: hfejzic@csusb.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06828-4
Received by editor(s): January 5, 2001
Received by editor(s) in revised form: March 27, 2002
Published electronically: October 15, 2002
Communicated by: David Preiss
Article copyright: © Copyright 2002 American Mathematical Society