Abstract
In an earlier paper, the concept of semigroups of self‐maps which are nearly commutative at a function g : X → X was introduced. We now continue the investigation, but with emphasis on the compact case. Fixed‐point theorems for such semigroups are obtained in the setting of semimetric and metric spaces.
Highlights
By a semigroup of maps we mean a family H of self-maps of a set X which is closed with respect to the composition of maps and includes the identity map
A semigroup H of self-maps of a set X is nearly commutative (n.c.) at g : X → X if and only if f ∈ H implies that there exists h ∈ H such that f g = gh
As in [6], we consider this concept in the context of generalized metric spaces, namely, semimetric spaces
Summary
By a semigroup of maps we mean a family H of self-maps of a set X which is closed with respect to the composition of maps and includes the identity map. In [6] we obtained fixed-point theorems for semigroups of maps by introducing the following concept. A semigroup H of self-maps of a set X is nearly commutative (n.c.) at g : X → X if and only if f ∈ H implies that there exists h ∈ H such that f g = gh.
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