Norm Estimates of the Pre-Schwarzian Derivatives for Functions with Conic-like Domains

Sidra Zafar, Abbas Kareem Wanas (), Mohamed Abdalla and Syed Zakar Hussain Bukhari
Additional contact information
Sidra Zafar: Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, AJK, Pakistan
Abbas Kareem Wanas: Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58001, Al-Qadisiyah, Iraq
Mohamed Abdalla: Mathematics Department, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Syed Zakar Hussain Bukhari: Department of Mathematics, Mirpur University of Science and Technology (MUST), Mirpur 10250, AJK, Pakistan

Mathematics, 2023, vol. 11, issue 11, 1-14

Abstract: The pre-Schwarzianand Schwarzian derivatives of analytic functions f are defined in U , where U is the open unit disk. The pre-Schwarzian as well as Schwarzian derivatives are popular tools for studying the geometric properties of analytic mappings. These can also be used to obtain either necessary or sufficient conditions for the univalence of a function f . Because of the computational difficulty, the pre-Schwarzian norm has received more attention than the Schwarzian norm. It has applications in the theory of hypergeometric functions, conformal mappings, Teichmüller spaces, and univalent functions. In this paper, we find sharp norm estimates of the pre-Schwarzian derivatives of certain subfamilies of analytic functions involving some conic-like image domains. These results may also be extended to the families of strongly starlike, convex, as well as to functions with symmetric and conjugate symmetric points.

Keywords: Möbius functions; upper half-plane; Schwarz function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/11/2490/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/11/2490/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:11:p:2490-:d:1158157

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().