Generalization of Jack's lemma for functions with fixed initial coefficient and its applications

Rogayeh Alavi, Saied Shams, Rasoul Aghalary

Abstract


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.

Keywords


Analytic functions, Differential subordination, Fixed initial coefficient, Meromorphic functions, Nunokawa's lemma, open-door lemma.

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2024.2.05

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