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., Fréchet Derivatives of Metric Projection Operator in Banach Spaces, Numerical Functional Analysis and Optimization, ISSN: 0163-0563 (Print) 1532-2467 (2025)
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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.