Starlike Functions Associated with Bernoulli’s Numbers of Second Kind

Abstract

The aim of this paper is to introduce a class of starlike functions that are related to Bernoulli’s numbers of the second kind. Let φBS(ξ)=ξeξ−12=∑n=0∞ξnBn2n!, where the coefficients of Bn2 are Bernoulli numbers of the second kind. Then, we introduce a subclass of starlike functions 𝟊 such that ξ𝟊′(ξ)𝟊(ξ)≺φBS(ξ). We found out the coefficient bounds, several radii problems, structural formulas, and inclusion relations. We also found sharp Hankel determinant problems of this class.

Keywords

• starlike functions
• subordination
• Bernoulli’s number of second kind
• radii problems
• inclusion results
• coefficient bounds