In this paper, two main results on the uniform stability of a resolvent family \(\{R_{h}(t)\}_{t\ge 0}\), depending on a parameter h are presented. First, we discuss a GGP type theorem on the resolvent family \(\{R_{h}(t)\}_{t\ge 0}\) and give some sufficient conditions on the uniform stability of \(\{R_{h}(t)\}_{t\ge 0}\). Then we prove that under some suitable conditions, the weak \(L^{p}\)-stability of \(\{R_{h}(t)\}_{t\ge 0}\) implies its uniform stability. Our results both essentially generalize previous work on the uniform stability of a family of \(C_{0}\)-semigroups \(\{T_{h}(t)\}_{t\ge 0}\) and a resolvent family \(\{R(t)\}_{t\ge 0}\), without depending on the parameter h. Examples are also given to illustrate our results.

在本文中，根据参数h，给出了关于解析子族\（\ {R_ {h}（t）\} _ {t \ ge 0} \）的一致稳定性的两个主要结果。首先，我们讨论旋变族\（\ {R_ {h}（t）\} _ {t \ ge 0} \）上的GGP型定理，并为\（\ {R_ { h}（t）\} _ {t \ ge 0} \）。然后，我们证明了一些合适的条件下，弱\（L ^ {P} \）的-稳定性\（\ {R_ {H}（t）的\} _ {吨\ GE 0} \）意味着其一致稳定性。我们的结果基本上都概括了以前关于\（C_ {0} \）-半群\（\ {T_ {h}（t）\} _ {t \ ge 0} \）和解析子的一致稳定性的工作。家庭\（\ {R（t）\} _ {t \ ge 0} \），而不取决于参数h。还给出了一些例子来说明我们的结果。