Involving Normal Families of Sharing Values of Higher-Order Derivative

Abstract

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. a_f,b_f,c_f are three finite non-zero complex numbers and a_f≠b_f. And satisfied 1) min{σ(0,a_f),σ(0,b_f),σ(a_f,b_f)}≥ε; 2) are independent of f; and f(z)=0⇔f^{(k )}(z)=a_f，f^{(k )}(z)=b_f⇒f(z)=c_f, . Then ℑ is normal in D.