Properties Of Some Class Of Analytic Functions Defined By Using Differential Subordinations

In chaper one, the author introduces a new subclass B₁(α,λ, A, B) of analytic functions. The subordination relationships, inclusion relationships, and some sufficient conditions for functions belonging to this class or its subclasses are discussed by making use of the techniques of Briot-Bouquet differential subordination.In chaper two, the Fekete-Szeg5 inequality for a subclass B(α,λ,p) of the class H of normalized analytic functions is discussed. For each f(z) = z + a₂z² + a₃z³ +…∈B(α,λ, p), the sharp upper bounds of[a₃-μa₂²] for any complex parameter # are obtained by the fundamental inequalities of analytic functions and analytical techniques, which generalize the related results of some authors.In chaper three, we introduces a subclass M(α,λ, p) of analytic functions and studies its some properties. The subordination relationships, inclusion relationships, coefficient estimates, the integral operator and covering theorem are proven here for each of the function class. Furthermore, some interesting Fekcte-Szego inequalities are also obtained. Some of the results, presented in this paper, would generalize the corresponding results of earlio, authors.