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Remarks on fixed points of rotative Lipschitzian mappings

Jarosław Górnicki (1999)

Commentationes Mathematicae Universitatis Carolinae

Let C be a nonempty closed convex subset of a Banach space E and T : C → C a k -Lipschitzian rotative mapping, i.eṡuch that ∥ T x - T y ∥ ≤ k · ∥ x - y ∥ and ∥ T n x - x ∥ ≤ a · ∥ x - T x ∥ for some real k , a and an integer n > a . The paper concerns the existence of a fixed point of T in p -uniformly convex Banach spaces, depending on k , a and n = 2 , 3 .

Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions

Luděk Zajíček (2014)

Commentationes Mathematicae Universitatis Carolinae

We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on Γ -almost everywhere Fréchet differentiability of Lipschitz functions on c 0 (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at Γ -almost every x at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are Γ -almost everywhere Fréchet differentiable....

Remarks on rich subspaces of Banach spaces

Vladimir Kadets, Nigel Kalton, Dirk Werner (2003)

Studia Mathematica

We investigate rich subspaces of L₁ and deduce an interpolation property of Sidon sets. We also present examples of rich separable subspaces of nonseparable Banach spaces and we study the Daugavet property of tensor products.

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