Bayoumi quasi-differential is not different from Frechet-differential

  1. Albiac, F. 1
  2. Ansorena, J.L. 2
  1. 1 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Central European Journal of Mathematics

ISSN: 1895-1074

Año de publicación: 2012

Volumen: 10

Número: 3

Páginas: 1071-1075

Tipo: Artículo

DOI: 10.2478/S11533-012-0031-9 SCOPUS: 2-s2.0-84859159046 WoS: WOS:000304651200021 GOOGLE SCHOLAR

Otras publicaciones en: Central European Journal of Mathematics

Resumen

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. © 2012 Versita Warsaw and Springer-Verlag Wien.