The Second Hankel Determinant for Starlike Functions of Order Alpha
D. K. Thomas
TL;DR
This paper establishes sharp bounds for the second Hankel determinant of functions that are starlike of a given order alpha within the unit disk, advancing the understanding of their geometric properties.
Contribution
It provides the first sharp bounds for the second Hankel determinant specifically for starlike functions of order alpha, a significant extension in geometric function theory.
Findings
Derived sharp bounds for the second Hankel determinant
Extended results to functions of arbitrary order alpha
Enhanced understanding of geometric properties of starlike functions
Abstract
Let f be analytic in D={z:|z|<1} with f(0)=0 and f'(0)=1. We give sharp bounds for the second Hankel determinant of f, when f is starlike of order alpha in D.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory