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Peer-reviewedCC BY 4.0Axioms

Sharp Bounds for Schippers–Schwarzian Derivatives via the Schur-Parameter Method

  • Hong Wang1
  • Xiaoyuan Wang2
  1. 1School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, China
  2. 2School of Mathematics and Systems Science, Liaocheng University, Liaocheng 252000, China
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Abstract

In the present paper, we derive sharp bounds for Schippers–Schwarzian derivatives of functions belonging to the two core Ma–Minda subclasses associated with the canonical half-plane majorant ψ(z)=1+z1−z: the convex class C(ψ) and starlike class S*(ψ), and the generalized Robertson class SPα(β). All derivations avoid Carathéodory coefficients cn; we only express the Taylor coefficients of Schwarz functions via Schur polynomials Fk(γ1,…,γk), then reduce each functional to a single-variable optimization, and construct explicit extremal Schwarz kernels as well as integral-form extremal univalent mappings.

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Cite

BibTeXRIS
BibTeX
@article{wang2026sharp,
  title = {{Sharp Bounds for Schippers–Schwarzian Derivatives via the Schur-Parameter Method}},
  author = {Hong Wang and Xiaoyuan Wang},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100783},
  url = {https://www.mdpi.com/2075-1680/15/10/783},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Sharp Bounds for Schippers–Schwarzian Derivatives via the Schur-Parameter Method
AU  - Hong Wang
AU  - Xiaoyuan Wang
PY  - 2026
DA  - 2026/10/19
JO  - Axioms
DO  - 10.3390/axioms15100783
UR  - https://www.mdpi.com/2075-1680/15/10/783
AB  - In the present paper, we derive sharp bounds for Schippers–Schwarzian derivatives of functions belonging to the two core Ma–Minda subclasses associated with the canonical half-plane majorant ψ(z)=1+z1−z: the convex class C(ψ) and starlike class S*(ψ), and the generalized Robertson class SPα(β). All derivations avoid Carathéodory coefficients cn; we only express the Taylor coefficients of Schwarz functions via Schur polynomials Fk(γ1,…,γk), then reduce each functional to a single-variable optimization, and construct explicit extremal Schwarz kernels as well as integral-form extremal univalent mappings.
SN  - 2075-1680
ER  -