On a Subclass of Harmonic Close-to-Convex Functions Generated by the Harmonic Error Function

We introduce a new subclass $\Xi P_{H}^{0}(\lambda)$ of harmonic mappings in the unit disk defined via a differential inequality involving the convolution operator generated by the harmonic error function. We show that this inequality directly produces harmonic close-to-convex mappings of order $\lambda$, thereby establishing a structural connection between the harmonic error function and harmonic close-to-convex geometry. For this class, we derive sharp coefficient bounds, a sufficient coefficient condition, and growth and distortion estimates. Furthermore, we prove that $\Xi P_{H}^{0}(\lambda)$ is closed under convex combinations and harmonic convolution. Several examples are provided to illustrate the applicability of the obtained results. These findings place the harmonic error function within the framework of harmonic close-to-convex theory and provide a systematic operator-based approach to generating such mappings.