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A mean value theorem for generalized Riemann derivatives
Author(s):
H.
Fejzic;
C.
Freiling;
D.
Rinne
Journal:
Proc. Amer. Math. Soc.
136
(2008),
569-576.
MSC (2000):
Primary 26A06, 26A24
Posted:
November 6, 2007
MathSciNet review:
2358497
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Abstract:
Functional differences that lead to generalized Riemann derivatives were studied by Ash and Jones in (1987). They gave a partial answer as to when these differences satisfy an analog of the Mean Value Theorem. Here we give a complete classification.
References:
-
- 1.
- J.M. Ash and R.L. Jones, Mean Value Theorems for Generalized Riemann Derivatives, Proc. Amer. Math. Soc., vol. 101, no. 2, October, 1987. MR 902539 (88i:26011)
- 2.
- J.M. Ash, A. E. Gatto, and S. Vági, A multidimensional Taylor's Theorem with minimal hypotheses, Colloq. Math., 60-61 (1990), 245-252. MR 1096374 (92b:26001)
- 3.
- Russell A. Gordon, The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Graduate Studies in Mathematics, vol. 4, American Mathematical Society, 1994. MR 1288751 (95m:26010)
- 4.
- E. Isaacson and H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 0201039 (34:924)
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Additional Information:
H.
Fejzic
Affiliation:
Department of Mathematics, California State University, San Bernardino, California 92407
Email:
hfejzic@csusb.edu
C.
Freiling
Affiliation:
Department of Mathematics, California State University, San Bernardino, California 92407
Email:
cfreilin@csusb.edu
D.
Rinne
Affiliation:
Department of Mathematics, California State University, San Bernardino, California 92407
Email:
drinne@csusb.edu
DOI:
10.1090/S0002-9939-07-08976-9
PII:
S 0002-9939(07)08976-9
Keywords:
Mean value theorem,
generalized derivatives
Received by editor(s):
March 28, 2006
Received by editor(s) in revised form:
October 10, 2006
Posted:
November 6, 2007
Additional Notes:
The second author was supported in part by NSF
Communicated by:
David Preiss
Copyright of article:
Copyright
2007,
American Mathematical Society
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