Certain new applications of Faber polynomial expansion for some new subclasses of $ \upsilon $-fold symmetric bi-univalent functions associated with $ q $-calculus

Abstract

<abstract><p>In this article, we define the $ q $-difference operator and Salagean $ q $-differential operator for $ \upsilon $-fold symmetric functions in open unit disk $ \mathcal{U} $ by first applying the concepts of $ q $-calculus operator theory. Then, we considered these operators in order to construct new subclasses for $ \upsilon $-fold symmetric bi-univalent functions. We establish the general coefficient bounds $ |a_{\upsilon k+1}| $ for the functions in each of these newly specified subclasses using the Faber polynomial expansion method. Investigations are also performed on Feketo-Sezego problems and initial coefficient bounds for the function $ h $ that belong to the newly discovered subclasses. To illustrate the relationship between the new and existing research, certain well-known corollaries of our main findings are also highlighted.</p></abstract>