Abstract
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
).