Abstract
In this paper, we show that there are no nontrivial surjective uniformly asymptotically regular mappings acting on a metric space, and we derive some consequences of this fact. In particular, we prove that a jointly continuous left amenable or left reversible semigroup generated by firmly nonexpansive mappings on a bounded \({\tau}\)-compact subset of a Banach space has a common fixed point, and we give a qualitative complement to the Markov–Kakutani theorem.
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Borzdyński, S., Wiśnicki, A. Applications of uniform asymptotic regularity to fixed point theorems. J. Fixed Point Theory Appl. 18, 855–866 (2016). https://doi.org/10.1007/s11784-016-0300-5
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DOI: https://doi.org/10.1007/s11784-016-0300-5