JournalszaaVol. 27, No. 1pp. 119–124

Remarks on Generalized Contractions

  • Dietrich Göhde

    Leipzig, Germany
Remarks on Generalized Contractions cover
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Abstract

The main result concerns an extension of Schauder's fixed point theorem to not necessarily continuous maps TT which satisfy

∥Tx−Ty∥≤a∥x−y∥+bmax⁡{∥Tx−x∥,∥Ty−y∥}with a≥0,  b∈(0,1) .\|Tx-Ty\| \le a \|x-y\|+b \max \{\|Tx-x\|, \|Ty-y\| \} \quad \text{with } a \ge 0, \; b \in (0,1)\,.

Cite this article

Dietrich Göhde, Remarks on Generalized Contractions. Z. Anal. Anwend. 27 (2008), no. 1, pp. 119–124

DOI 10.4171/ZAA/1347