Editing Banach space (section)

==Derivatives==

Several concepts of a derivative may be defined on a Banach space. See the articles on the [[Fréchet derivative]] and the [[Gateaux derivative]] for details. 
The Fréchet derivative allows for an extension of the concept of a [[total derivative]] to Banach spaces. The Gateaux derivative allows for an extension of a [[directional derivative]] to [[locally convex]] [[topological vector space]]s. 
Fréchet differentiability is a stronger condition than Gateaux differentiability. 
The [[quasi-derivative]] is another generalization of directional derivative that implies a stronger condition than Gateaux differentiability, but a weaker condition than Fréchet differentiability.