On applications of the extended Jack's lemma

UDC 517.5 We introduce and study a class (α,β) comprising analytic functions associated with a sector domain, where α,β∈(0,1]. By using the extended version of Jack's lemma, we deduce the Open–Door lemma sufficient conditions for functions to be in (α,β). Furthermore, we present special cases of our results that are in agreement with known results.