Fixed point theorems for discontinuous operators. (English) Zbl 0705.47044
The authors show that any operator T in a Banach space satisfying
\[
\| Tx-Ty\| \leq a\| x-y\| +b\| x-Tx\| +b\| y- Ty\|
\]
(a,b\(\geq 0)\) has a unique fixed point. For similar discussions, see the second author’s paper in Pac. J. Math. 123, 189-196 (1986; Zbl 0549.47028).
Reviewer: J.Appell
MSC:
47H10 | Fixed-point theorems |