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Zeitschrift für Analysis und ihre Anwendungen

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Volume 27, Issue 1, 2008, pp. 119–124
DOI: 10.4171/ZAA/1347

Published online: 2008-03-31

Remarks on Generalized Contractions

Dietrich Göhde

The main result concerns an extension of Schauder's fixed point theorem to not necessarily continuous maps $T$ which satisfy $$\|Tx-Ty\| \le a \|x-y\|+b \max \{\|Tx-x\|, \|Ty-y\| \} \quad \text{with } a \ge 0, \; b \in (0,1)\,. $$

Keywords: Fixed points, generalized contractions, nonexpansive mappings

Göhde Dietrich: Remarks on Generalized Contractions. Z. Anal. Anwend. 27 (2008), 119-124. doi: 10.4171/ZAA/1347