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...

For a closed nowhere dense subset C of ∂D a bounded univalent holomorphic function f on D is found such that C equals the cluster set of its fixed points.

In the present paper, we consider a generalised subclass of analytic functions involving arithmetic, geometric and harmonic means. For this function class we obtain an inclusion result, Fekete-Szegö inequality and coefficient bounds for bi-univalent functions.

In the present paper, we investigate some important properties of a new class of univalent holomorphic functions by using Komatu operator. For example coefficient estimates, extreme points, neighborhoods and partial sums. 2000 Mathematics Subject Classification: 30C45, 30C80.

In this paper, we estimate the second and third Maclaurin's coefficients of certain subclass of bi-univalent functions in open unit disk defined by Caputo Fractional calculus operator and also indicate certain special cases.

We consider the linear functional Re(a 3 + a 2) for 2 iRon the set of normalized univalent functions in the unit disk and use the result to disprove a conjecture of Bombieri.

We consider the class of univalent functions defined by the conditions f(z)/z ≠ 0 and |(z/f(z))′′| ≤α,|z|< 1, where f(z)= z+··· is analytic in |z|< 1 and 0<α≤ 2.

Let f(z) be any transcendental entire function. Let r, denote the absolute value of the zero z. of f '(z) which is nearest to the origin. Alander, Erdö's and Renyi, and Polya have investigated the relation between r, and the growth of the function /(z). Let s, denote the ... fz largest disk about the origin where / (z) is univalent. Boas, Levinson, and Polya have obtained some relations between...

which are analytic in the open unit disc U {z ∈ C : |z| < 1} on the complex plane C. Let S, S∗ α , C α 0 ≤ α < 1 denote the subclasses of A consisting of functions that are univalent, starlike of order α, and convex of order α in U, respectively. In particular, the classes S∗ 0 S∗ and C 0 C are the familiar classes of starlike and convex functions inU, respectively. A function f ∈ C α if Re 1 z...