Normal Criterion of Meromorphic Functions Whose Derivatives Omit a Holomorphic Function

P. Yang; L. Wu; J. Yang

doi:10.3103/s1068362326700044

June 1, 2026Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)

Normal Criterion of Meromorphic Functions Whose Derivatives Omit a Holomorphic Function

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Key Points

To establish conditions under which a family of meromorphic functions is normal based on the behavior of their derivatives.
Examined a family of meromorphic functions with zeros of multiplicity at least k+1.
Considered a non-constant holomorphic function whose zeros are also multiple.
Analyzed the condition that the k-th derivative of any function in the family does not equal the holomorphic function at any point.
If each function's k-th derivative differs from the holomorphic function at every point, the family is normal at points where the holomorphic function has zeros.

Implication

This research demonstrates normality in a family of meromorphic functions based on their derivatives, indicating important implications for complex analysis.

Abstract

Let k≥ 2 be a positive integer. Let F be a family of meromorphic functions in D , whose zeros have multiplicity at least $$k+1$$ . Let h(≡ 0) be a holomorphic function in D , whose zeros are multiple. If each f and each z∈ D , f⁽ᵏ⁾(z)≠ h(z) , then F is normal at points for which $$h(z)=0$$ .

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Cite This Study

Yang et al. (2026) studied this question.

synapsesocial.com/papers/6a3a2194111626ef22ab6622 https://doi.org/10.3103/s1068362326700044

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Normal Criterion of Meromorphic Functions Whose Derivatives Omit a Holomorphic Function

Key Points

Implication

Abstract

Discussion

Cite This Study

Normal Criterion of Meromorphic Functions Whose Derivatives Omit a Holomorphic Function

Key Points

Implication

Abstract

Discussion

Cite This Study

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