Generalization of Jack’s Lemma for Functions With Fixed Initial Coefficient and Its Applications
DOI:
https://doi.org/10.24193/subbmath.2024.2.05Keywords:
Analytic functions, differential subordination, fixed initial coefficient, meromorphic functions, Nunokawa’s lemma, open-door lemmaAbstract
In this paper, by using the theory of differential subordination, we will generalize Jack’s lemma for functions with fixed initial coefficient. Then extensions of the well-known open-door lemma for analytic and meromorphic functions with fixed initial coefficient are given. Also, we are considering some applications of the extension of Jack’s lemma.
Mathematics Subject Classification (2010): 30C45, 30C80.
Received 07 December 2021; Accepted 17 March 2022
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