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Peer-reviewedCC BY 4.0Axioms

Geometric Characteristics of Meromorphic Starlike Functions Linked with a Novel Image Domain

  • Muhammad Umar Farooq1
  • Muhammad Arif1
  • Hari M. Srivastava2,3,4,5,6,7
  • Mohamed Biomy8
  • Muhammad Abbas1
8 affiliations
  1. 1Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan
  2. 2Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
  3. 3Department of Medical Research, China Medical University Hospital, Taichung 40402, Taiwan
  4. 4Center for Converging Humanities, Kyung Hee University Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
  5. 5Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
  6. 6Section of Mathematics, International Telematic University Uninettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy
  7. 7Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan
  8. 8Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
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Abstract

The present article is mainly concerned with radius problems for a newly defined subclass of meromorphic starlike functions having the punctured open unit disk as its domain. This subclass is introduced by using differential subordination with the generalized tangent function q0(z)=1+tan(μz) as the superordinate function. Sharp radius constants are established for starlikeness and convexity of order ρ, and the MStanμ*-radii are determined for several notable subclasses, including Janowski-type classes and classes represented through quotients of meromorphic functions. We further introduce a tangent-order subclass MStanμ,σ*, obtain its representation formula, and derive corresponding starlikeness and convexity radius estimates. Finally, the superordinate tangent function is studied from the viewpoint of conformal mapping theory: its conformality, inverse mapping, boundary parametrization, disk inclusions, and conformal range criterion are established and illustrated graphically.

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Cite

BibTeXRIS
BibTeX
@article{farooq2026geometric,
  title = {{Geometric Characteristics of Meromorphic Starlike Functions Linked with a Novel Image Domain}},
  author = {Muhammad Umar Farooq and Muhammad Arif and Hari M. Srivastava and Mohamed Biomy and Muhammad Abbas},
  journal = {Axioms},
  year = {2026},
  month = nov,
  doi = {10.3390/axioms15110821},
  url = {https://www.mdpi.com/2075-1680/15/11/821},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Geometric Characteristics of Meromorphic Starlike Functions Linked with a Novel Image Domain
AU  - Muhammad Umar Farooq
AU  - Muhammad Arif
AU  - Hari M. Srivastava
AU  - Mohamed Biomy
AU  - Muhammad Abbas
PY  - 2026
DA  - 2026/11/04
JO  - Axioms
DO  - 10.3390/axioms15110821
UR  - https://www.mdpi.com/2075-1680/15/11/821
AB  - The present article is mainly concerned with radius problems for a newly defined subclass of meromorphic starlike functions having the punctured open unit disk as its domain. This subclass is introduced by using differential subordination with the generalized tangent function q0(z)=1+tan(μz) as the superordinate function. Sharp radius constants are established for starlikeness and convexity of order ρ, and the MStanμ*-radii are determined for several notable subclasses, including Janowski-type classes and classes represented through quotients of meromorphic functions. We further introduce a tangent-order subclass MStanμ,σ*, obtain its representation formula, and derive corresponding starlikeness and convexity radius estimates. Finally, the superordinate tangent function is studied from the viewpoint of conformal mapping theory: its conformality, inverse mapping, boundary parametrization, disk inclusions, and conformal range criterion are established and illustrated graphically.
SN  - 2075-1680
ER  -