On \(\beta\)-differentiability of norms

Authors

  • Valeriu Anisiu "Babeş Bolyai" University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat332-768

Keywords:

convex function, differentiability, bornology, subgradient
Abstract views: 185

Abstract

In this note we give some characterizations for the differentiability with respect to a bornology of a continuous convex function. The special case of seminorms is treated. A characterization of this type of differentiability in terms of the subgradient of the function is also obtained.

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References

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Rainwater, J., Yet more on the differentiability of convex functions, Proc. Amer. Math. Soc., 103, no. 3, pp. 773-778, 1988,https://doi.org/10.1090/s0002-9939-1988-0947656-7 DOI: https://doi.org/10.1090/S0002-9939-1988-0947656-7

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Zajicek, L., On the differentiation of convex functions in finite and infinite dimensional spaces, Czechoslovak Math. J., 29, pp. 340-348, 1979. DOI: https://doi.org/10.21136/CMJ.1979.101616

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Published

2004-08-01

How to Cite

Anisiu, V. (2004). On \(\beta\)-differentiability of norms. Rev. Anal. Numér. Théor. Approx., 33(2), 141–148. https://doi.org/10.33993/jnaat332-768

Issue

Vol. 33 No. 2 (2004)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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