JournalszaaVol. 27 , No. 1DOI 10.4171/zaa/1347

Remarks on Generalized Contractions

  • Dietrich Göhde

    Leipzig, Germany
Remarks on Generalized Contractions cover

Abstract

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

TxTyaxy+bmax{Txx,Tyy}with a0,  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)\,.