Faber Polynomial Coefficient Bounds for$m$-Fold Symmetric Analytic and Bi-univalent Functions Involving$q$-Calculus

Abstract

In our present investigation, by applying q -calculus operator theory, we define some new subclasses of m -fold symmetric analytic and bi-univalent functions in the open unit disk U = z ∈ ℂ : z < 1 and use the Faber polynomial expansion to find upper bounds of a m k + 1 and initial coefficient bounds for a m + 1 and a 2 m + 1 as well as Fekete-Szego inequalities for the functions belonging to newly defined subclasses. Also, we highlight some new and known corollaries of our main results.

Some New Applications of the q-Analogous of Differential and Integral Operators for New Subclasses of q-Starlike and q-Convex Functions

“…Using the basics of q-calculus, Zang et al [27] constructed a generalized conic domain and studied a new category of q-starlike functions in this context. Geometric function theory (GFT) and q-calculus theory both have been the subject of a great deal of research by numerous mathematicians to date (for details, see [28][29][30][31][32][33][34]). It has been established that time-scale calculus, a more general branch of mathematics, involves quantum calculus.…”