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

Muhammad Shafiq,Hari M Srivastava,Maslina Darus,Nazar Khan,Samiha Kiran,Qazi Zahoor Ahmad

doi:10.3390/sym12061043

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.

Highlights

Introduction and DefinitionsThe calculus without the notion of limits is called quantum calculus; it is usually called q-calculus or q-analysis
By the P class of analytic functions, p(z) in U is denoted, in which normalization conditions are given as follow:
Güney et al [20] and Uçar [12], we will define a new subclass SL(k, q) of starlike functions associated with the k-Fibonacci numbers

Summary

Introduction

Introduction and DefinitionsThe calculus without the notion of limits is called quantum calculus; it is usually called q-calculus or q-analysis. By the P class of analytic functions, p(z) in U is denoted, in which normalization conditions are given as follow: Let q ∈ (0, 1) the q-number [λ]q is given by Were obtained in such earlier works as, for example, in [17,18] for various subclasses of the normalized analytic function class A.

Results

Conclusion