Applications of uniform asymptotic regularity to fixed point theorems

作者：Borzdynski Slawomir^*; Wisnicki Andrzej

来源：Journal of Fixed Point Theory and Applications, 2016, 18(4): 855-866.

DOI：10.1007/s11784-016-0300-5

• Asymptotic regularity
• fixed point
• firmly nonexpansive mapping
• averaged mapping
• amenable semigroup
• weak topologies
• Markov-Kakutani theorem
• affine retraction

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 -compact subset of a Banach space has a common fixed point, and we give a qualitative complement to the Markov-Kakutani theorem.

• 出版日期2016-12