### On the structure of fixed-point sets of uniformly lipschitzian mappings

#### Abstract

It is shown that the set of fixed points of any $k$-uniformly lipschitzian

mapping in a uniformly convex space is a retract of a domain if $k$ is close

to $1$.

mapping in a uniformly convex space is a retract of a domain if $k$ is close

to $1$.

#### Keywords

Uniformly lipschitzian mapping; retraction; fixed point; uniformly convex space

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