Real Analysis Exchange

Are cone-monotone functions generically intermediately differentiable?.

Xianfu Wang

Full-text: Open access

Abstract

On a separable Banach space, we show that a cone-monotone function is generically intermediate differentiable provided its Dini-derivatives are finite along every direction and the cone has nonempty interior.

Article information

Source
Real Anal. Exchange, Volume 29, Number 2 (2003), 729-738.

Dates
First available in Project Euclid: 7 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149698535

Mathematical Reviews number (MathSciNet)
MR2083808

Zentralblatt MATH identifier
1079.46515

Subjects
Primary: 46G05: Derivatives [See also 46T20, 58C20, 58C25]

Keywords
Separable Banach space cone-monotone function pointwise Lipschitz function intermediate derivative

Citation

Wang, Xianfu. Are cone-monotone functions generically intermediately differentiable?. Real Anal. Exchange 29 (2003), no. 2, 729--738. https://projecteuclid.org/euclid.rae/1149698535


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References

  • J. M. Borwein, X. Wang, Cone monotone functions: differentiability and continuity, Canadian Journal of Mathematics, submitted, available as Preprint 2003:209 at http://www.cecm.sfu.ca/Preprints03/preprints03.html.
  • J. M. Borwein, J. V. Burke, and A. S. Lewis, Differentiability of cone-monotone functions on separable spaces, Proc. Amer. Math. Soc., to appear.
  • A. M. Bruckner, J. B. Bruckner, and B. S. Thomson, Real Analysis, Prentice-Hall, 1997.
  • M. Fabian and D. Preiss, On intermediate differentiability of Lipschitz functions on certain Banach spaces, Proc. Amer. Math. Soc., 113 (1991), 733–740.
  • J. R. Giles and S. Sciffer, Generalizing generic differentiability properties from convex to locally Lipschitz functions, J. Math. Anal. Appl., 188 (1994), 833–854.
  • L. Zajicek, {A note on intermediate differentiability of