涉及高阶导数分担值的正规族  

Involving Normal Families of Sharing Values of Higher-Order Derivative

作　　者：王皓然 杨祺[1] 

机构地区：[1]新疆师范大学数学科学学院,新疆 乌鲁木齐

出　　处：《理论数学》2023年第3期445-452,共8页Pure Mathematics

摘　　要：分析了两类涉及变动分担值以及高阶导数的函数族正规性。应用Pang-Zalcman引理,分别讨论了两个涉及高阶导数的全纯函数f以及亚纯函数g分担值的正规定则,并且将固定分担值推广到了依赖于f与g的分担值,得到了两类新的正规定则。令ℑ为D上一全纯函数族,af,bf,cf为3个非零有穷复数,af≠bf,满足:1)min{σ(0,af),σ(0,bf),σ(af,bf)}≥ε;2)相对于f独立;若对于任意的f∈ℑ,f的零点重级至少为k,且f(z)=0⇔f(k )(z)=af,f(k )(z)=bf⇒f(z)=cf,则ℑ在复数域D内正规。Two classes of function family regularity involving higher-order derivative variable sharing values are discussed. Applying the Pang-Zalcman lemma, normality criterions for sharing values of holo-morphic functions f and meromorphic functions g which involving higher-order derivatives are dis-cussed respectively, and the fixed sharing values are generalized to the sharing values which de-pendent on f and g, hence two normality criterion are obtained. Let be a family of holomorphic function in a domain D, for every f∈ℑ, the zeros of f have multiplicities at least k. af,bf,cf are three finite non-zero complex numbers and af≠bf. And satisfied 1) min{σ(0,af),σ(0,bf),σ(af,bf)}≥ε;2) are independent of f;and f(z)=0⇔f(k )(z)=af,f(k )(z)=bf⇒f(z)=cf, . Then ℑ is normal in D.

关 键 词：正规族 全纯函数 分担值 亚纯函数 

分 类 号：G63[文化科学—教育学]