Inclusion Relations, Coefficient Bounds, and Subordination Properties for Uniformly Multivalent Functions Subordinate to Conic Domains

In this paper, we introduce and systematically investigate four novel subclasses of uniformly multivalent (k-valent) analytic functions defined in the open unit disk, which are associated with a generalized linear operator and subordinate to conic domains. By employing the structural recurrence properties of the operator and the theory of first-order differential subordinations, we establish inclusion relation- ships for these subclasses with respect to the operator parameters. Furthermore, we obtain sharp upper bounds for the initial Taylor–Maclaurin coefficients, derive a sharp solution to the Fekete–Szeg˝o problem, and evaluate an upper bound for the second Hankel determinant. Differential subordination criteria providing suffi- cient conditions for class membership and invariance properties under a generalized Bernardi-type integral operator are also demonstrated. The results established herein extend and unify numerous existing theorems in geometric function theory.