On Row Differential Inequalities Related to Normality and Quasi-normality

Tomer Manket, Shahar Nevo

Research output: Contribution to journalArticlepeer-review

Abstract

We study connections between a new type of linear differential inequalities and normality or quasi-normality. We prove that if C>0, k≥1 and a0(z),⋯,ak-1(z) are fixed holomorphic functions in a domain D, then the family of the holomorphic functions f in D, satisfying for every z∈D (Formula presented.) is quasi-normal in D. For the reversed sign of the inequality we show the following: Suppose that A,B∈C, C>0 and F is a family of meromorphic functions f satisfying for every z∈D (Formula presented.) and also at least one of the families f/f:f∈F or f′′/f:f∈F is normal. Then F is quasi-normal in D.

Original languageEnglish
JournalComputational Methods and Function Theory
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

Keywords

  • 30A10
  • 30D45
  • Differential inequalities
  • Normal families
  • Quasi-normal families

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