A Conjecture on H₃(1) For Certain Starlike Functions

2022/08/05 by Neha Verma, Verma, Neha, S. Sivaprasad Kumar +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2208.02975

openalex publication_date 2022/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture concerning the third Hankel determinant, proposed in ``Anal. Math. Phys., https://doi.org/10.1007/s13324-021-00483-7", which states that |H₃(1)|≤ 1/9 is sharp for the class S_\wp^*=\zf'(z)/f(z) \prec φ(z):=1+ze^z\. In addition, we also establish bounds for sixth and seventh coefficient, and |H₄(1)| for functions in S_\wp^*. The general bounds for two and three-fold symmetric functions related to the Ma-Minda classes S^*(φ) of starlike functions are also obtained.

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