Norm estimation for pre-Schwarzian and Schwarzian derivatives of some univalent functions

Authors

  • Xiaobin Wu Nanjing University of Science and Technology, China
  • Wanghao Zhu Nanjing University of Science and Technology, China

DOI:

https://doi.org/10.3842/umzh.v77i6.8599

Keywords:

pre-Schwarzian derivative, Schwarzian derivative, starlike functions, convex functions

Abstract

UDC 517.5

Our purpose is to obtain estimates for the norms of  Schwarzian  and pre-Schwarzian derivatives of strongly starlike functions and strongly convex functions of order $\alpha$ and type $\beta.$ In addition, we present an example of a function $f \in S^*(\alpha, \beta)$ that  cannot be $k$-quasiconformally extended for any $k < \alpha(1 - \beta).$

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 6, 2025.

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Published

01.08.2025

Issue

Vol. 77 No. 6 (2025)

Section

Research articles

License

Copyright (c) 2025 Xiaobin Wu, Wanghao Zhu

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Wu, Xiaobin, and Wanghao Zhu. “Norm Estimation for Pre-Schwarzian and Schwarzian Derivatives of Some Univalent Functions”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 6, Aug. 2025, pp. 445–446, https://doi.org/10.3842/umzh.v77i6.8599.