quasi total double roman domination in trees

A quasi total double roman dominating function (qtdrd-function) on a graph $g=(v(g),e(g))$ is a function $f:v(g)longrightarrow{0,1,2,3}$ having the property that textrm{(i)} if $f(v)=0$, then vertex $v$ must have at least twoneighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$; textrm{(ii)} if $f(v)=1$, then vertex $v$ has at least one neighbor $w$ with $f(w)geq2$, and textrm{(iii)} if $x$ is an isolated vertex in the subgraph induced by the set of vertices assigned non-zero values, then $f(x)=2$. the weight of a qtdrd-function $f$ is the sum of its function values over the whole vertices, and the quasi total double roman domination number $gamma_{qtdr}(g)$ equals the minimum weight of a qtdrd-function on $g$. in this paper, we show that for any tree $t$ of order $nge 4$, $gamma_{qtdr}(t)le n+frac{s(t)}{2}$, where $s(t)$ is the number of support vertices of $t$,  that improves a known bound.