Some properties of the mapping $T_μ$ introduced by a representation in Banach and locally convex spaces
Ebrahim Soori · arXiv (Cornell University) · 2017
Let $ \sc=\{T_{s}:s\in S\} $ be a representation of a semigroup $S$. First, we prove that the mapping $T_μ$ introduced by a mean on a subspace of $l^{\infty}(S)$ has many properties of the mappings in the representation $ \sc$, in Banach spaces. Then we consider a directed graph and then we define a $Q$-$G$-nonexpansive mapping in locally convex spaces and show that $T_μ$ is a $Q$-$G$-nonexpansive mapping if $T_{s}$ is a $Q$-$G$-nonexpansive mapping for each $s\in S$. Then we define $Q$-$G$-attractive point of $ \sc$ and show if a point $a$ is a $Q$-$G$-attractive point of $ \sc$ then $a$ is a $Q$-$G$-attractive point of $T_μ$.