A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity z f ′(z)/ f (z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and di...

Double integral operators which were considered by S. S. Miller and P. T. Mocanu Integral Transform. Spec. Funct. 19 2008 , 591–597 are discussed. In order to show the analytic function f z is starlike of order β in the open unit disk U, the theory of differential subordinations for analytic functions is applied. The object of the present paper is to discuss some interesting conditions for f z ...

Also let S, S∗ β , CV β , and K denote, respectively, the subclasses of A0 consisting of functions which are univalent, starlike of order β, convex of order β cf. 1 , and close-to-convex cf. 2 in U. In particular, S∗ 0 S∗ and CV 0 CV are the familiar classes of starlike and convex functions in U cf. 2 . Given f and g inA, the function f is said to be subordinate to g in U if there exits a funct...

A b s t r a c t. A tree is said to be starlike if exactly one of its vertices has degree greater than two. We show that almost all starlike trees are hyperbolic, and determine all exceptions. If k is the maximal vertex degree of a starlike tree and λ 1 is its largest eigenvalue, then √ k ≤ λ 1 < k/ √ k − 1. A new way to characterize integral starlike trees is put forward.

For p-valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional |a p2 − μa 2 p1 | related to the Fekete-Szegö problem are given.

In an earlier paper [l] the writer showed the development of a variational method for starlike functions and applied this method to a general class of extremal problems connected with the coefficients of the function. It is the purpose of this paper to study the classes of extremal problems to which this variational method can be applied and to make some remarks as to its utility. The class S* ...

We determine the sufficient conditions for function f(z) = z + a2z2 ... to be starlike of order 1/2, which shows also starlikeness f.

We extend the “Extension after Restriction Principle” for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.

Classes of multivalent functions analogous to certain classes of univalent starlike functions are defined and studied. Estimates on coefficients and distortion are made, using a variety of techniques. 1. Let St denote the class of all functions/(z) = z + . . . analytic, univalent and starlike in the unit disc U. Such functions satisfy the condition Re(z/'(z)//(z)) >0,zGU. The problem of definin...

Ruscheweyh‘and She&Small proved the P6lya-Schoenberg conjecture that the class of convex analytic functions is closed under convolution or Hadamard product. They also showed that clos&o-convexity is preserved under convolution with convex analytic functions. In this note, we investigate harmonic analogs. Beginning with convex analytic functions, we form certain harmonic functions which preserve...