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

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Frigon M.

Banach Center Publications

2007

tom 77

nr 1

89-114

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.