On Certain Classes of Biharmonic Mappings Defined by Convolution

Abstract

We introduce a class of complex-valued biharmonic mappings, denoted by $B{H}^0({\varphi }_k;\sigma ,a,b)$, together with its subclass $TB{H}^0({\varphi }_k;\sigma ,a,b)$, and then generalize the discussions in Ali et al. (2010) to the setting of $B{H}^0({\varphi }_k;\sigma ,a,b)$ and $TB{H}^0({\varphi }_k;\sigma ,a,b)$ in a unified way.