An Upper Bound of the Third Hankel Determinant for a Subclass of q-Starlike Functions Associated with k-Fibonacci Numbers

Abstract

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.

Sharp Bounds of the Coefficient Results for the Family of Bounded Turning Functions Associated with a Petal-Shaped Domain

“…where S * ð1/2Þ indicates the starlike function family of order 1/2: We would also like to acknowledge the research provided by Mahmood et al [40] in which they examined the third Hankel determinant in the q-analog for a subfamily of starlike functions and for more contribution of such type families, see [41,42]. In the present article, our aim is to calculate the sharp bounds of some of the problems related to Hankel determi-nant for the class BT s of bounded turning functions connected with a petal-shaped domain.…”

A note on generalized q-difference equations for general Al-Salam–Carlitz polynomials

“…In conclusion, we find it to be worthwhile to remark that some potential further applications of the methodology and findings, which we have been presented here by means of q-analysis and q-calculus, can be found in the study of zeta and q-zeta functions as well as their related functions of analytic number theory (see, for example, [43,44]; see also [9]) and also in the study of analytic and univalent functions of geometric function theory via number-theoretic entities (see, for example, [45]).…”

Third Hankel Determinant Problem for Certain Subclasses of Analytic Functions Associated with Nephroid Domain

“…Whose third Hankel was evaluated by Shafiq et al [30]. Further related work on the subject the reader is referred to [31,32,33]. Motivated from above discussed work on the topic we investigate |H 3,1 (f )| for classes of functions defined in the relations (1.4) and (1.5).…”