Fixed point theorems for nonlinear operators with and without monotonicity in partially ordered Banach spaces.

Ding, Hui-Sheng; Liang, Jin; Xiao, Ti-Jun

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Singlevaluedness of monotone operators on subspaces of GSG spaces

Martin Heisler (1996)

Commentationes Mathematicae Universitatis Carolinae

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We extend Zajíček’s theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a $σ$ -cone supported set.