An application of Jack's lemma for the minimum point

TL;DR

This paper applies a theorem related to the minimum value of |f(z)| for analytic functions, expanding on prior results and deriving new corollaries using Jack's lemma.

Contribution

It introduces new applications and corollaries of a known theorem on the minimum modulus of analytic functions using Jack's lemma.

Findings

Derived new corollaries from the existing theorem.

Extended the application of Jack's lemma to minimum point analysis.

Provided insights into the behavior of |f(z)| for analytic functions.

Abstract

For the analytic function f(z), H. Shiraishi and S. Owa (Stud. Univ. Babes-Bolyai Math. 55(2010), 207-211) have shown a theorem for the minimum value of |f(z)|. In this paper, we discuss an application of this theorem and some corollaries.