On extensions of the Jack and open-door lemmas

In the present paper, we apply the theory of differential subordination to extend the famous Jack lemma for analytic functions. Also, using this extension we will produce new versions of the open-door lemma for analytic functions, and utilizing them some simple conditions for starlikeness of analyti...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2023; no. 1; pp. 38 - 17
Main Authors Alavi, R., Shams, S., Aghalary, R., Cho, N. E.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 10.03.2023
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Analytic functions
Applications of Mathematics
Differential subordination
Jack’s lemma
Mathematical analysis
Mathematics
Mathematics and Statistics
Meromorphic functions
Open-door lemma
Open-door lemma
30C45
Analytic functions
Jack’s lemma
Meromorphic functions
Differential subordination
30C80
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Summary:In the present paper, we apply the theory of differential subordination to extend the famous Jack lemma for analytic functions. Also, using this extension we will produce new versions of the open-door lemma for analytic functions, and utilizing them some simple conditions for starlikeness of analytic and meromorphic functions are obtained. Our results improve and extend the earlier results investigated in the literature.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-02925-1