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...

The authors investigate interesting properties of certain subclasses of meromorphically multivalent functions which are defined by means of extended multiplier transformations. MSC 2010. 34C40.

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.

In a recent paper [2], G. R. Blakley raised a question about the decomposition of a ^-valent starlike function into the product of two ^-valent starlike functions. It is the purpose of this note to prove the conjecture of Blakley. Definition 1. The function/(z), regular in |z| <1, is said to be in the class S(p, m), where p and m are positive integers with p^m, if and only if (1) there exists a...

and Applied Analysis 3 On the other hand, for a function f defined by 1.6 and in the class C p, α , Lemma 1.2 yields ap 1 ≤ p ( p − α ( p 1 )( p 1 − α . 1.10 In view of the coefficient inequalities 1.9 and 1.10 , it would seem to be natural to introduce and study here two further classes T ∗ ε p, α and Cε p, α of analytic and p-valent functions, where T ∗ ε p, α denotes the subclass of T ∗ p, α...

In this article, we use the concept of symmetric q-calculus and convolution in order to define a q-differential operator for multivalent functions. This is an extension classical Ruscheweyh differential operator. By using technique subordination, derive several interesting applications newly defined

The object of the present paper is to drive some properties of certain class Kn,p(A,B) of multivalent analytic functions in the open unit disk E.

Making use of the principle of differential subordination, we investigate some inclusion relationships of certain subclasses of multivalent analytic functions associated with the Wright generalized hypergeometric function.

The purpose of this paper is to derive subordination and superordination results involving differential operator for multivalent analytic functions in the open unit disk. These are applied obtain sandwich results. Our extend corresponding previously known