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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.

47H10 Fixed-point theorems
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