Mediterranean Journal of Mathematics

, Volume 13, Issue 4, pp 1997–2010 | Cite as

Boundary Conditions for 1-Set Contractions Maps in Banach Spaces

  • Smaïl Djebali
  • Karima Hammache


In this work, we have obtained some fixed point theorems for 1-set contractions under some boundary conditions such as the Leray–Schauder condition and the interior condition. Our results complement those obtained in Djebali and Hammache (Fixed Point Theory, to appear, 2014) and Garcia-Falset (Math. Nachr. 283(12):1736–1757, 2010) and improve (Petryshyn in Arch. Ration. Mech. Anal. 40:312–328 1971).


Nonexpansive mappings 1-set contraction mappings ψ-expansive mappingss α–ψ-expansive mappings Kuratowski measure of noncompactness Leray–Schauder condition interior condition fixed point 

Mathematics Subject Classification

Primary 47H09 Secondary 47H10 47J25 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Laboratoire “Théorie du Point Fixe et Applications”École Normale SupérieureKoubaAlgeria

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