LAUSR

Let $$A>1$$A>1 be a constant and $$\mathcal {F}$$F be a family of meromorphic functions defined in a domain D. For each $$f\in \mathcal {F}$$f∈F, f has only zeros of multiplicity at least 3 and satisfies the following conditions: (1) $$|f^{\prime \prime \prime }(z)|\le A|z|$$|f″′(z)|≤A|z| when $$f(z)=0$$f(z)=0; (2) $$f^{\prime \prime \prime }(z)\ne z$$f″′(z)≠z; (3) all poles of f are multiple. In this paper, we characterize the non-normal sequences of $$\mathcal {F}$$F.