On applications of the extended Jack's lemma - Kumar, S. Sivaprasad; Yadav, Pooja (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5We introduce and study a class ${\bf\mathcal{G}}(α,β)$ comprising analytic functions associated with a sector domain, where $α,β\in(0,1]$. By using the extended version of Jack's lemma, we deduce the Open–Door lemma sufficient conditions for functions to be in ${\bf\mathcal{G}}(α,β)$. Furthermore, we present special cases of our results that are in agreement with known results.