In 1955, Waadeland considered the class of m-fold symmetric starlike functions of the form f_m(z)=z+∑^∞_n=1 (z)a_mn+1z^mn+1; m≥1; |z|< 1 and obtained the sharp coefficient bounds |a_mn+1|≤ [(2/m+n-1)/[(n!)(2/m-1)!]. Pommerenke in 1962, proved the same coefficient bounds for m-fold symmetric close-to-convex functions. Nine years later, Keogh and Miller confirmed the same bounds for the class of m-fold symmetric Bazilevic functions. Here we will show that these bounds can be improved even further for the m-fold symmetric bi-close-to-convex functions. Moreover, our results improve those corresponding coefficient bounds given by Srivastava et al that appeared in 7(2) (2014) issue of this journal. A function is said to be bi-close-to-convex in a simply connected domain if both the function and its inverse map are close-to-convex there.

Tbilisi Mathematical Journal, Vol. 9(2) (2016), pp. 75-82