Two New Criteria for Normal Families

Two New Criteria for Normal Families

Let a0, . . . , ak−1 be analytic functions on a domain Ω. Let F be a family of meromorphic functions f on Ω such that f 6= 0 and f (k) + ak−1f (k−1) + . . . + a0f 6= 0 on Ω, for all f ∈ F . Then {f ′/f : f ∈ F} is a normal family. Furthermore, let a0, . . . , ak−1 be meromorphic functions on a domain Ω. Let F be a family of meromorphic functions f on Ω such that f 6= 0, f ′ 6= 0 and f (k) + ak−...

Some Normal Criteria for Families of Meromorphic Functions

In the paper, we study the normality of families of meromorphic functions related a Hayman Conjecture. We consider whether a family meromorphic functions F is normal in D, if for each function f in F , f ′ + af = b has at most one zero, where n is a positive integer, a and b = 0 are two finite complex numbers. Some examples show that the conditions in our results are best possible.

Normal Criteria for Families of Meromorphic Function concerning Shared Values

Let k be a positive integer and let F be a family of meromorphic functions in the plane domain D all of whose zeros with multiplicity at least k. Let P = apz p + · · ·+a2z +z be a polynomial, ap, a2 6= 0 and p = deg(P ) ≥ k+2. If, for each f, g ∈ F , P (f)G(f) and P (g)G(g) share a non-zero constant b in D, where G(f) = f (k) + H(f) be a differential polynomial of f satisfying w deg |H ≤ k l+1 ...

Normal Criteria of Function Families Concerning Shared Values

Two New Non-AFR Criteria for Depicting Strength Differential Effect (SDE) in Anisotropic Sheet Metals

The issue of pressure sensitivity of anisotropic sheet metals is investigated with introducing two new non-AFR criteria which are called here linear and non-Linear pressure sensitive criteria. The yield and plastic potential functions of these criteria are calibrated with directional tensile/compressive yield stresses and directional tensile Lankford coefficients, respectively. To determine unk...