Bayoumi quasi-differential is not different from Fréchet-differential

• Autorzy: Fernando Albiac , José Ansorena
• Języki publikacji: EN

Abstrakty

EN

Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception, since it could hinder making headway in this already hard enough subject. To that end we show that Bayoumi quasi-differentiability, when properly defined, is the same as Fréchet differentiability, and that some of his alleged applications are wrong.

Słowa kluczowe

EN

Quasi-Banach space; F-space; Quasi-differentiability (also Bayoumi-differentiability or pq-differentiability); Fréchet differentiability

Kategorie tematyczne

• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1071-1075

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Fernando Albiac

• Universidad Pública de Navarra

autor

José Ansorena

• Universidad de La Rioja

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0031-9