On Applications of Extended Jack's Lemma

Abstract

We introduce and study the class $\mathcal{G}(\hat{I}\pm ,{\hat{I}}^2)$ comprising analytic functions associated with a sector domain, where $\hat{I}\pm ,{\hat{I}}^2\in (0,1]$. Using the extended version of Jack's lemma, we deduce Open-Door lemma type sufficient conditions for functions to be in $\mathcal{G}(\hat{I}\pm ,{\hat{I}}^2)$. Furthermore, we point out special cases of our results that align with known results.

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