INITIAL COEFFICIENT BOUNDS FOR NEW SUBCLASSES OF <i>M</i>-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS WITH BOUNDED BOUNDARY ROTATION

In the present article, the authors introduce the concept of <i>m</i>-fold symmetric bi-univalent functions with bounded boundary rotation and introduce three new subclasses of <i>m</i>-fold symmetric bi-univalent functions. For the newly defined classes, the authors obtain first two initial coefficient bounds. Furthermore, the Fekete-Szegö bounds are also obtained for these three new classes of functions. Apart from many new results and new corollaries, the results in this article also improves earlier existing bounds available in the literature.