Bi-Univalent Functions Involving Error Function Subordinating to Limacon Domain

By using the analytic structure of the error function, the geometric depth of limacon type \mbox{domains}, the algebraic strength of the Hankel determinant and Fekete- Szeg\”{o} functional we introduce in this study a new subclass of bi-univalent functions. This subclass is defined by subordination to the normalized error function and limacon mappings. Bounds for the initial Taylor- Maclaurin coefficients of functions in this subclass are \mbox{determined}. Furthermore the Fekete–Szeg\”{o} functional and Hankel determinant for this subclass is also addressed.