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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
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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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