M-fold symmetric biunivalent functions defined by Gegenbauer polynomials: novel subclasses and coefficient bounds

Abstract

In this paper, we use Gegenbauer polynomials to define a novel subclass of holomorphic biunivalent functions which are m-fold symmetric inside U={s:s in C and |s|<1}. We compute estimates on initial bounds |d_m+1|, |d_2m+1| and the Fekete-Szego inequalities for functions that are a member of the stated subclasses. Also, several novel results are obtained as special cases of our results.