The power of Gâteaux differentiability

Vitor Neves ()
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Vitor Neves: Universidade de Aveiro, Departamento de Matemática

Chapter 18 in The Strength of Nonstandard Analysis, 2007, pp 253-270 from Springer

Abstract: Abstract The search for useful non standard minimization conditions on C 1 functionals defined on Banach spaces lead us to a very simple argument which shows that if a C 1 function f : E → F between Banach spaces is actually Gâteaux differentiable on finite points along finite vectors, then it is uniformly continuous on bounded sets if and only if it is lipschitzian on bounded sets. The following is a development of these ideas starting from locally convex spaces.

Keywords: Banach Space; Convex Space; Standard Function; Nonstandard Analysis; Finite Point (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/978-3-211-49905-4_18

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