Bounds for initial MacLaurin coefficients of a subclass of bi-univalent functions associated with subordination

Abstract

In this paper, we investigate the bounds of the coe¢ cients for new subclasses of analytic and bi-univalent functions in the open unit disc de…ned by subordination. The coe¢ cients bounds presented in this paper would generalize and improve those in related works of several earlier authors

Coefficient bounds for bi-univalent classes defined by Bazilevič functions and convolution

“…2Þ ( see [2]); (3) W j;1Àq;2;0 ðf à hÞ ¼ W j;q ðf à hÞ ðf ; h 2 P ; j ! 1 and 0 q\1Þ (see [8] and [12]); (4) W 1;1Àq;2;0 ðf à z 1Àz Þ ¼ W q ðf Þ ðf 2 P and 0 q\1Þ ( see [22] and [11]); (5) W r;1Àq;2;0 ðf à z 1Àz Þ ¼ W q;r ðf Þ ðf 2 P ; r ! 0 and 0 q\1Þ (see [9]).…”