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...

There is broad interest in designing nanostructured materials that can interact with cells and regulate key downstream functions. In particular, materials with nanoscale features may enable control over multivalent interactions, which involve the simultaneous binding of multiple ligands on one entity to multiple receptors on another and are ubiquitous throughout biology. Cellular signal transdu...

Abstract In this article we prove meromorphic continuation of weighted zeta functions $$Z_f$$ Z f in the framework open hyperbolic systems by using meromorphically continued restricted resolvent Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016). We obta...

In this paper we obtain some majorization results for some classes of multivalent functions defined by certain differential operator. Mathematics subject classification (2010): 30C45.

This paper aims to provide sufficient conditions for starlikeness and convexity of Hadamard product (convolution) certain multivalent analytic functions with positive real parts. Moreover, the a integral operator other convolution results are also considered.