Some properties of a new subclass of m-fold symmetric bi-Bazilevic functions associates with modified sigmoid function

Abstract

In the present article, the author investigates some properties of fractional analytic function $g_{m}(z)^{\alpha}$, belonging to two new subclasses of m-fold symmetric starlike and convex functions in the open unit disk. In addition, properties of certain new subclass $T^{\alpha}_{m, n}(\beta)$, of m-fold symmetric bi-Bazilevic functions associated with modified sigmoid functions are considered while several other corollaries follow as simple consequences.