On the second Hankel determinant of concave functions

2015/12/10 by Rintaro Ohno, Toshiyuki Sugawa, Ohno, Rintaro +1
Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1512.03146

openalex publication_date 2015/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we will discuss the Hankel determinants H(f) =a₂a₄-a₃² of order 2 for normalized concave functions f(z)=z+a₂z²+a₃z³+… with a pole at p∈(0,1). Here, a meromorphic function is called concave if it maps the unit disk conformally onto a domain whose complement is convex. To this end, we will characterize the coefficient body of order 2 for the class of analytic functions φ(z) on |z|<1 with |φ|<1 and φ(p)=p. We believe that this is helpful for other extremal problems concerning a₂, a₃, a₄ for normalized concave functions with a pole at p.

Citations

• On the Second Hankel Determinant of Mean Univalent Functions

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