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On uniform Opial condition and uniform Kadec-Klee property in Banach and metric spaces. (English) Zbl 0854.47035
Recently it has been shown that many classical or nonclassical Banach spaces enjoy a uniform property with respect to a given topology. This enables the authors to prove a fixed point result via well known theorems. In this work we show that there is a more general property that reduces to the main conclusion of these results. Therefore, these conclusions should not be seen as particular results in particular spaces. We will also define and study properties such as Opial condition, Kadec-Klee and ergodic properties in hyperbolic metric spaces.

MSC:
47H10 Fixed-point theorems
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