On the fourth coefficient of univalent functions with bounded boundary rotation

On Certain Analytic Functions of Bounded Boundary Rotation

In this paper we introduce certain analytic functions of boundary rotation bounded by k1r which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk E = {z E C Izi < I} , which are also of bounded boundary rotation.

Coefficient Estimates for Univalent Functions

Coefficient ConditionsFor Certain Univalent Functions

Some subclasses of analytic functions f(z) in the open unit disk U are introduced. In the present paper, Some interesting sufficient conditions, including coefficient inequalities related close-to-convex functions f(z) of order α with respect to a fixed starlike function g(z) and strongly starlike functions f(z) of order μ in U, are discussed. Several special cases and consequences of these coe...

A Variational Method for Functions of Bounded Boundary Rotation

Let / be a function analytic in the unit disc, properly normalized, with bounded boundary rotation. There exists a Stieltjes integral representation for 1 +zf"(z)jf'(z). From this representation, and in view of a known variational formula for functions of positive real part, a variational formula is derived for functions of the form q(z) = l +zf"(z)jf'(z). This formula is for functions of arbit...

Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...