# zbMATH — the first resource for mathematics

A fixed point theorem in Banach space. (English) Zbl 0538.47035
Summary: A proof of the following theorem is given: Let C be a closed convex subset of a Banach space and let T:$$C\to C$$ satisfy the condition $$\| Tx-Ty\| \leq a\| x-y\| +b\| Tx-x\| +c\| Ty-y\|$$ with $$a+b+c=1$$. Then T has a fixed point.

##### MSC:
 47H10 Fixed-point theorems