Advances on the coefficient bounds for m-fold symmetric
bi-close-to-convex functions
J. M. Jahangiri, S. G. Hamidi
In 1955, Waadeland considered the class of m-fold symmetric starlike
functions of the form
fm(z)=z+∑∞n=1
(z)amn+1zmn+1;
m≥1; |z|< 1 and obtained the sharp coefficient bounds |amn+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
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