Abstract
In this paper, we introduce three new subclasses of m-fold symmetric holomorphic functions in the open unit disk U, where the functions f and f−1 are m-fold symmetric holomorphic functions in the open unit disk. We denote these classes of functions by FSΣ,mp,q,s(d), FSΣ,mp,q,s(e) and FSΣ,mp,q,s,h,r. As the Fekete-Szegö problem for different classes of functions is a topic of great interest, we study the Fekete-Szegö functional and we obtain estimates on coefficients for the new function classes.
Highlights
Introduction and Preliminary ResultsLet A denote the family of functions of the form ∞ f (z) = z +Citation: Breaz, D.; Cotîrlă, L.-I
K =2 which are analytic in the open unit disk U = {z ∈ C : |z| < 1} and normalized by the conditions f (0) = 0, f 0 (0) = 1
Let Σ denote the class of all bi-univalent functions in U given by (1)
Summary
Let Σ denote the class of all bi-univalent functions in U given by (1). A function is said to be m-fold symmetric if it has the following normalized form: ; The important results about the m-fold symmetric analytic bi-univalent functions are given in [3,4,5,6,7]. Many authors obtained coefficient estimates of bi-univalent functions in the articles [2,14,15,16,17,18,19,20,21,22,23,24,25].
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