Application of Differential Subordinations to the Arithmetic–Geometric Means by Using an Operator

This study investigates differential subordination involving arithmetic and geometric mean approaches associated with a previously introduced operator. While earlier studies considered cases where the dominant function was convex or linear, the present work extends these results by examining differential subordinations for specific classes of convex functions. The paper establishes new criteria and subordination relationships for analytic functions defined through the operator, thereby providing a unified framework that connects the arithmetic–geometric mean inequalities with the theory of differential subordination. These findings contribute new insights and enhance the understanding of operator-based approaches in geometric function theory.