Study of quantum calculus for a new subclass of $ q $-starlike bi-univalent functions connected with vertical strip domain

Abstract

<abstract><p>In this study, using the ideas of subordination and the quantum-difference operator, we established a new subclass $ \mathcal{S} ^{\ast }\left(\delta, \sigma, q\right) $ of $ q $-starlike functions and the subclass $ \mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right) $ of $ q $-starlike bi-univalent functions associated with the vertical strip domain. We examined sharp bounds for the first two Taylor-Maclaurin coefficients, sharp Fekete-Szegö type problems, and coefficient inequalities for the function $ h $ that belong to $ \mathcal{S}^{\ast }\left(\delta, \sigma, q\right) $, as well as sharp bounds for the inverse function $ h $ that belong to $ \mathcal{S}^{\ast }\left(\delta, \sigma, q\right) $. We also investigated some results for the class of bi-univalent functions $ \mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right) $ and well-known corollaries were also highlighted to show connections between previous results and the findings of this paper.</p></abstract>

New Uses of q-Generalized Janowski Function in q-Bounded Turning Functions

“…Zang and colleagues [17] employed q-calculus symbols and subordination methods to establish a broad conic region, which was then utilized to analyze the category of q-starlike functions. Several authors have recently conducted studies on the categories of q-starlike functions, as referenced in articles [18][19][20][21][22][23]. In order to research different categories of analytic and bi-univalent functions, the initial step is to establish the definition of the q-difference operator.…”