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The fixed point property in a Banach space isomorphic to c 0

Costas Poulios (2014)

Commentationes Mathematicae Universitatis Carolinae

We consider a Banach space, which comes naturally from c 0 and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings defined on weakly compact, convex sets.

The fixed point property in Musielak-Orlicz sequence spaces

Harold Bevan Thompson, Yunan Cui (2001)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an H-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the Kadec-Klee property, the uniform Kadec-Klee property and to be nearly uniformly convex. We show that a Musielak-Orlicz sequence space equipped with the Orlicz norm has the fixed point property if and only if it is reflexive....

The fixed point theorem and the boundedness of solutions of differential equations in the Banach space

František Tumajer (1993)

Mathematica Bohemica

The properties of solutions of the nonlinear differential equation x ' = A ( s ) x + f ( s , x ) in a Banach space and of the special case of the homogeneous linear differential equation x ' = A ( s ) x are studied. Theorems and conditions guaranteeing boundedness of the solution of the nonlinear equation are given on the assumption that the solutions of the linear homogeneous equation have certain properties.

The form boundedness criterion for the relativistic Schrödinger operator

Vladimir Maz'ya, Igor Verbitsky (2004)

Annales de l’institut Fourier

We establish necessary and sufficient conditions on the real- or complex-valued potential Q defined on n for the relativistic Schrödinger operator - Δ + Q to be bounded as an operator from the Sobolev space W 2 1 / 2 ( n ) to its dual W 2 - 1 / 2 ( n ) .

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