By using the method of differential subordination, we obtain some sufficient conditions for strongly p-valent starlikeness.

* Correspondence: [email protected] Department of Mathematics, Yangzhou University, Yangzhou, 225002, PR China Full list of author information is available at the end of the article Abstract By using the method of differential subordinations, we derive certain properties of meromorphically multivalent functions. 2010 Mathematics Subject Classification: 30C45; 30C55.

By making use of subordination between analytic functions and the Dziok-Srivastava operator, we introduce a new subclass of multivalent analytic functions. Such results as inclusion relationship, integral presentations and convolution properties for this function class are proved.

The main purpose of the present paper is to derive a new criterion for mul-tivalent starlike functions by applying Jack's lemma.

For analytic and multivalent functions f (z) and p(z) in the open unit disk U, a subordi-nation theorem due to Littlewood (1925) which was called the integral mean is applied. Some simple examples for our results are also considered.

Multivalent protein-carbohydrate interactions that are mediated by sugar-binding proteins, i.e., lectins, have been implicated in a myriad of intercellular recognition processes associated with tumor progression such as galectin-mediated cancer cellular migration/metastatic processes. Here, using a modified ELISA, we show that glycodendrimers bearing mixtures of galactosides, lactosides, and N-...

Let A(p) be the class of functions f : f(z) = z + ∑∞ j=1 ajz p+j analytic in the open unit disc E. Let, for any integer n > −p, fn+p−1(z) = z p (1−z)n+p . We define f (−1) n+p−1(z) by using convolution ? as fn+p−1(z) ? f (−1) n+p−1(z) = z (1−z)n+p . A function p, analytic in E with p(0) = 1, is in the class Pk(ρ) if ∫ 2π 0 ∣∣∣Rep(z)−ρ p−ρ ∣∣∣ dθ ≤ kπ, where z = re, k ≥ 2 and 0 ≤ ρ < p. We use t...

The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all a...

We use a property of the Bernardi operator in the theory of the Briot–Bouquet differential subordinations to prove several theorems for the classes VpkðH;A;BÞ of multivalent analytic functions defined by using the Dziok–Srivastava operator H. Some of these results we obtain applying the convolution property due to Rusheweyh. We take advantage of the Miller–Mocanu lemma to improve the earlier re...