numerical range of a sum of weighted composition operators on the weighted bergman spaces

Suppose that $varphi$ is an analytic self-map of the open unit disk $mathbb{d}$ and $psi$ is a bounded analytic function on $mathbb{d}$. the weighted composition operator $c_{psi,varphi}$ is the operator on the weighted bergman spaces $a_{alpha}^{2}$ given by $c_{psi,varphi}f=psi fcircvarphi$ for any $fin a_{alpha}^{2}$. if $varphi_1,varphi_2,...,varphi_n$ are linear fractional non-automorphisms and $psi_{1},psi_{2},...,psi_{n} $ are bounded analytic functions, under some conditions, we obtain a subset of the numerical range of $c_{psi_1,varphi_1}+c_{psi_2,varphi_2}+...+c_{psi_n,varphi_n}$ on $a_{alpha}^{2}$ and determine when zero lies in the interior of its numerical range.