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

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

In this paper, we use <i>q</i>-derivative operator to define a new class of <i>q</i>-starlike functions associated with <i>k</i>-Fibonacci numbers. This newly defined class is a subclass of class <inline-formula> <math display="inline"> <s...

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Bibliographic Details
Main Authors:	Muhammad Shafiq, Hari M. Srivastava, Nazar Khan, Qazi Zahoor Ahmad, Maslina Darus, Samiha Kiran
Format:	Article
Language:	English
Published:	MDPI AG 2020-06-01
Series:	Symmetry
Subjects:	starlike functions subordination <i>q</i>-Differential operator <i>k</i>-Fibonacci numbers
Online Access:	https://www.mdpi.com/2073-8994/12/6/1043

Description
Summary:	In this paper, we use <i>q</i>-derivative operator to define a new class of <i>q</i>-starlike functions associated with <i>k</i>-Fibonacci numbers. This newly defined class is a subclass of class <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">A</mi> </semantics> </math> </inline-formula> of normalized analytic functions, where class <inline-formula> <math display="inline"> <semantics> <mi mathvariant="script">A</mi> </semantics> </math> </inline-formula> is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.
ISSN:	2073-8994