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.
L., Strict Fré chet Differentiability of Metric Projection Operator in Hilbert Spaces, J
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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.