A Study of q-analogue of the analytic characterization of Limacon functions

Abstract

The investigation of Ma and Minda classes of functions associated with q-calculus has been on increase in recent times. Newly, limac ¸on functions, the classes of starlike and convex limac ¸on functions were initiated and investigated in the literature. As a result, the present article is aimed to present the q-analogue of the limac ¸on functions and utilize it to establish the classes of starlike and convex limac ¸on functions that are correlated with quantum calculus. To this end, the geometric characterization of these functions is examined. Moreover, radius, subordination and some other related results with these novel classes are verified. Overall, some consequences of our investigations are also illustrated.

Sharp Bounds of the Fekete–Szegö Problem and Second Hankel Determinant for Certain Bi-Univalent Functions Defined by a Novel q-Differential Operator Associated with q-Limaçon Domain

“…In this article, we introduce and investigate a subclass of analytical and bi-univalent functions defined by a new q-differential operator associated with the q-limaçon domain, which is inspired by the work of Saliu et al [48,49]. Definition 3. f ∈ ΛM σ,j,n α,δ (q), suppose the following conditions are met:…”