Defines generalized critical points and ordered extrema in partially ordered Banach spaces and proves that order monotonicity of mappings is characterized by their Gateaux or Frechet derivatives.
A., A simple Theory of differential calculus, Transactions of the American mathematical society, Volume 293, Number 2, February (1986)
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Differentiation and Ordered Optimization in Banach Spaces
Defines generalized critical points and ordered extrema in partially ordered Banach spaces and proves that order monotonicity of mappings is characterized by their Gateaux or Frechet derivatives.