Some Coefficient Inequalities of q-Starlike Functions Associated with Conic Domain Defined by q-Derivative

Abstract

This article deals with q-starlike functions associated with conic domains, defined by Janowski functions. It generalizes the recent study of q-starlike functions while associating it with the conic domains. Certain renowned coefficient inequalities in connection with the previously known ones have been included in this work.

Hankel and Toeplitz Determinants for a Subclass of q-Starlike Functions Associated with a General Conic Domain

“…where p j (j = 1, 2, 3) are positive and are the coefficients of the functions p k (z) defined by (6). Each of the above results is sharp for the function g (z) given by…”

“…In fact, subjected to the conic domain Ω k (k 0), Kanas and Wiśniowska (see [3,4]; see also [6]) studied the corresponding class k-S T of k-starlike functions in U (see Definition 1 below). For fixed k, Ω k represents the conic region bounded successively by the imaginary axis (k = 0), by a parabola (k = 1), by the right branch of a hyperbola (0 < k < 1), and by an ellipse (k > 1).…”

Janowski Type q-Convex and q-Close-to-Convex Functions Associated with q-Conic Domain

“…Note that, when q → 1, then, the class k − U K q (λ, α, β, γ) reduces into the well-known class that is defined in (see [40]).…”

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

“…Moreover, in 2018, Kwon et al [38] improved the bound of Zaprawa for f ∈ S * and proved that |H 3,1 ( f )| ≤ 8/9, but it is not yet the best possible. The authors in [39][40][41] contributed in a similar direction by generalizing different families of univalent functions with respect to symmetric points. In 2018, Kowalczyk et al [42] and Lecko et al [43] obtained the sharp inequalities:…”