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Authors: ROGAYEH ALAVI, SAIED SHAMS, RASOUL AGHALARY.
Received 07 December 2021; Accepted 17 March 2022.
pp. 317-334
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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 consider some applications of the extension of Jack’s lemma.
Mathematics Subject Classification (2010): 30C45, 30C80.
Keywords: Analytic functions, Differential subordination, Fixed initial coefficient, Meromorphic functions, Nunokawa’s lemma, open-door lemma.
