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

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.