The Mazur intersection property for families of closed bounded convex sets in Banach spaces
Pradipta Bandyopadhyaya (1992)
Colloquium Mathematicae
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Pradipta Bandyopadhyaya (1992)
Colloquium Mathematicae
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We prove that the initial value problem x’(t) = f(t,x(t)), is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.
Acu, Mugur (2004)
General Mathematics
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Binyamin Schwarz, Uri Srebro (1996)
Banach Center Publications
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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on which are balls with respect to the complex norm in are those centered at the origin.