Martin Väth

Fixed point theorems and fixed point index for countably condensing maps

It is proved that there exists a fixed point index theory for operators which are condensing on the countable subsets of the space only. Even weaker compactness assumptions on countable subsets suffice, e.g. conditions with respect to classes of measures of noncompactness, or if measures of noncompactness of countable noncompact sets are not preserved (not necessarily decreased). As an application, we prove a generalization of the Fredholm alternative.

Coincidence Points of Function Pairs Based on Compactness Properties

Existence theorems for the equation F(x)=\varphi (x) are proved when F is a function with “good” surjective properties and \varphi satisfies certain compactness conditions on countable subsets of the space. Also results for certain homotopic perturbations of the equation are obtained. The results lead to various fixed point theorems of Darbo type for F=id , but they are also applicable if F acts between different spaces. Also the inclusions F(x)\in \varphi (x) (resp. F(x)\subseteq \varphi (x) ) for multivalued functions \varphi (resp. F and \varphi ) are studied. There are some connections with the theory of 0 -epi maps.

An axiomatic approach to a coincidence index for noncompact function pairs

We prove that there is a coincidence index for the inclusion

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

F(x)\in\Phi(x)

Topological analysis : from the basics to the triple degree for nonlinear Fredholm inclusions

when

Integration theory : a second course

\Phi

Calculation of Lefschetz and Nielsen numbers in hyperspaces for fractals and dynamical systems

is convex-valued and satisfies certain compactness assumptions on countable sets. For

Nuclear factor of activated T cells—A transcription factor family as critical regulator in lung and colon cancer

F

Continuity and Differentiability of Multivalued Superposition Operators with Atoms and Parameters I

we assume only that it provides a coincidence index for single-valued finite-dimensional maps (e.g.

Two topological definitions of a Nielsen number for coincidences of noncompact maps

F