Functiones et Approximatio Commentarii Mathematici

Differentiability of strongly paraconvex vector-valued functions

Stefan Rolewicz

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Abstract

In the paper the notion of strongly $\alpha(\cdot)$-$K$-paraconvex functions is introduced. It is shown that a strongly $\alpha(\cdot)$-$K$-paraconvex function defined on a convex set contained in a Banach space $X$ with values in $\mathbb{R}^n$ is: (a) Fréchet differentiable on a dense $G_{\delta}$-set provided $X$ is an Asplund space, (b) Gateaux differentiable on a dense $G_{\delta}$-set provided $X$ is separable.

Article information

Source
Funct. Approx. Comment. Math., Volume 44, Number 2 (2011), 273-277.

Dates
First available in Project Euclid: 22 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.facm/1308749130

Digital Object Identifier
doi:10.7169/facm/1308749130

Mathematical Reviews number (MathSciNet)
MR2841185

Zentralblatt MATH identifier
1230.46037

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

Keywords
strongly $\alpha(\cdot)$-$K$-paraconvexity Gateaux and Fréchet differentiability

Citation

Rolewicz, Stefan. Differentiability of strongly paraconvex vector-valued functions. Funct. Approx. Comment. Math. 44 (2011), no. 2, 273--277. doi:10.7169/facm/1308749130. https://projecteuclid.org/euclid.facm/1308749130


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References

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