A mean value theorem for generalized Riemann derivatives
HTML articles powered by AMS MathViewer
- by H. Fejzić, C. Freiling and D. Rinne PDF
- Proc. Amer. Math. Soc. 136 (2008), 569-576 Request permission
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
- J. M. Ash and R. L. Jones, Mean value theorems for generalized Riemann derivatives, Proc. Amer. Math. Soc. 101 (1987), no. 2, 263–271. MR 902539, DOI 10.1090/S0002-9939-1987-0902539-2
- J. Marshall Ash, A. Eduardo Gatto, and Stephen Vági, A multidimensional Taylor’s theorem with minimal hypothesis, Colloq. Math. 60/61 (1990), no. 1, 245–252. MR 1096374, DOI 10.4064/cm-60-61-1-245-252
- Russell A. Gordon, The integrals of Lebesgue, Denjoy, Perron, and Henstock, Graduate Studies in Mathematics, vol. 4, American Mathematical Society, Providence, RI, 1994. MR 1288751, DOI 10.1090/gsm/004
- Eugene Isaacson and Herbert Bishop Keller, Analysis of numerical methods, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0201039
Additional Information
- H. Fejzić
- 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
- Received by editor(s): March 28, 2006
- Received by editor(s) in revised form: October 10, 2006
- Published electronically: November 6, 2007
- Additional Notes: The second author was supported in part by NSF
- Communicated by: David Preiss
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 569-576
- MSC (2000): Primary 26A06, 26A24
- DOI: https://doi.org/10.1090/S0002-9939-07-08976-9
- MathSciNet review: 2358497