A Study in some Classes of Bi Univalent Functions
عقيل كتاب الخفاجي, مريم غثوان كاظم موسى
كلية التربية للعلوم الصرفة-جامعة بابل · العراق
A function is analytic at if its derivative exists at as well as at in some neighborhoods of each point . It is analytical in region D if at every point of region D it is analytical. We say F is a entier function in every point in the complex plane if it is analytical C. Furthermore, an open unit disc *||+function f analytic is said to be univalent if it is not used twice in the same value i.e.,()().In other words, is one-to-one (or injective) mapping of onto another domain and we say that a function is said to be bi-univalent function if both and are univalent.The aim of this work is to introduce and investigates a several classes of analytic and univalent functions as well as classes of bi-univalent functions and it has some different problems, such as, some properties for analytic univalent functions associated with generalized Mittag-Leffler functions, certain properties of a subclass of analytic functions based on differential operator, Chebyshev polynomials coefficients for bi-univalent function .Finally, define bi-univalent functions using a sigmoid activation function with bounded boundary rotation in the bi-univalent functions class.