Abstract
In the Jack’s lemma it is considered q(z), an analytic function in \(|z|<1\) with \(q(0)=0\) for which |q(z)| attains its maximum value on the disc \(|z|\le r<1\) at the point \(z_0\), \(|z_0|=r\). Then \(z_0q'(z_0)=kq(z_0)\) and \(k\ge 1\). In this paper we try to say more about the number k in a generalizations of this lemma, where we consider \(\max |\arg \{q(z)\}|\) or \(\min |\mathfrak {Re} \{q(z)\}|\) instead of |q(z)|. In these cases q(z) has another normalization at the origin.
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Nunokawa, M., Piejko, K. & Sokół, J. Applications of Jack’s lemma. Anal.Math.Phys. 14, 15 (2024). https://doi.org/10.1007/s13324-024-00872-8
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DOI: https://doi.org/10.1007/s13324-024-00872-8