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Fixed point and continuation results for contractions in metric and gauge spaces

M. Frigon (2007)

Banach Center Publications

We present an overview of generalizations of Banach's fixed point theorem and continuation results for contractions, i.e., results establishing that the existence of a fixed point is preserved by suitable homotopies. We will consider single-valued and multi-valued contractions in metric and in gauge spaces.

Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

R.P. Agarwal, D. O'Regan, D.R. Sahu (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

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