Bregman nonexpansive type actions of semitopological semigroups

Let $S$ be a semitopological semigroup, and let $C$ be a nonempty closed convex subset of a reflexive Banach space. Under some amenability conditions on $S$, we provide existence results of fixed points for several Bregman nonexpansive type actions $S\times C\to C$, $(s,x)\mapsto T_s x$, of $S$ on $C$. The mappings $T_s$ we discuss include those being Bregman generalized hybrid, Bregman nonspreading, and Bregman left asymptotically nonexpansive.