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A remark on fixed point theorems for Lipschitzian mappings. (English) Zbl 0806.47050

Let \(C\) be a bounded closed convex subset of a \(p\)-uniformly convex Banach space \((p>1)\) and \((a_{n,k})\) be a strongly ergodic matrix. The author proves that every map \(T: C\to C\) satisfying \[ \liminf_{n\to\infty} \inf_ m \sum^ \infty_{k=1} a_{n,k}\| T^{k+m}\|^ p< 1+c \] \((c>0)\) has a fixed point in \(C\).

MSC:

47H10 Fixed-point theorems
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