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: 165

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.

Downloads

Download data is not yet available.

References

Deville, R., Godefroy, G. and Zizler,V., Renormings and Smoothness in Banach Spaces, Monographs and Surveys in Pure and Appl. Math., Longman, 64, 1993.

Giles, J. R., Convex Analysis with Application to Differentiation of Convex Functions, Research Notes in Math., 58, Pitman, 1982.

Phelps, R. R., Convex Functions, Monotone Operators and Differentiability, 2nd ed., Springer, 1993, https://doi.org/10.1007/978-3-540-46077-0 DOI: https://doi.org/10.1007/978-3-540-46077-0

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

Sireţchi, Gh., Functional Analysis, Universitatea Bucureşti, 1982 (in Romanian).

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

Downloads

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

License

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

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.