Multivalent Functions Research Articles

Starlikeness and related properties of certain integral operator for multivalent functions

In this paper, the authors introduce a new general integral operator for multivalent functions. The new sufficient conditions for the operator to have some properties are obtained. We obtain many known results as corollaries.

Convolution properties for meromorphically multivalent functions involving generalized Bessel functions

Some novel convolution properties for meromorphically multivalent functions associated with the generalized Bessel functions of the first kind are derived.

Properties of a New Subclass of Meromorphically Multivalent Functions with Linear Operator

Properties of a New Subclass of Meromorphically Multivalent Functions with Linear Operator

Conditions for Starlikeness of Multivalent Functions

A function f(z) meromorphic in a domain \(D\subset {\mathbb {C}}\) is said to be p-valent in D if for each w the equation \(f(z)=w\) has at most p roots in D, where roots are counted in accordance with their multiplicity, and there is some v such that the equation \(f(z)=v\) has exactly p roots in D. We prove some new sufficient conditions for functions to be p-valently starlike in the unit disc.

Some subclasses of meromorphically multivalent functions associated with the Dziok-Srivastava operator

We introduce two new subclasses Hp,k(?,A,B) and Qp,k(?,A,B) of meromorphically multivalent functions associated with the Dziok-Srivastava operator which is a special case of the Srivastava-Wright operator. Distortion inequalities, partial sums and convolutional theorems for Hp,k(?,A,B) and Qp,k(?,A,B) are obtained.

Coeffcient bounds for a subclass of multivalent functions of reciprocal order

The aim of this paper is to introduce a new subclass of multivalent functions of complex order and to study some interesting properties such as coeffcient estimates, suffciency criteria, Fekete-Szego inequality, inclusion result and integral preserving property for this newly defined class.

Certain Subclasses of Multivalent Functions Defined by Higher-Order Derivative

In this paper, we define and study some subclasses of multivalent analytic functions of higher order in the unit disc. These classes generalize some classes previously studied. We obtain coefficient inequalities, distortion theorems, extreme points, and integral mean inequalities. We derive some results as special cases.

A family of meromorphically multivalent functions which are starlike with respect to k-symmetric points

A family of meromorphically multivalent functions which are starlike with respect to k-symmetric points

Some Convolution Properties of Multivalent Analytic Functions

In this paper, we introduce a new subclass of multivalent functions associated with conic domain in an open unit disk. We study some convolution properties, su cient condition for the functions belonging to this new class.

Some Marx-Strohhacker type results for a class of multivalent functions

Some Marx-Strohhacker type results for a class of multivalent functions

On certain multivalent functions involving the generalized Srivastava-Attiya operator

On certain multivalent functions involving the generalized Srivastava-Attiya operator

Operator on Hilbert space and its application to certain multivalent functions with fixed point associated with hypergeometric function

By applying hypergeometric operator on Hilbert space, the author introduces a new class of meromorphic multivalent functions with an arbitrary fixed point omega. Properties such as coefficient inequalities, distortion bounds and extreme points were derived. Furthermore, the effect of this operator on functions in this class was also investigated.

Mast cells as effector cells of innate immunity and regulators of adaptive immunity

Mast cells are widely distributed in human organs and tissues and they are particularly abundant at major body interfaces with the external environment such as the skin, the lung and the gastrointestinal tract. Moreover, mast cells are located around blood vessels and are highly represented within central and peripheral lymphoid organs. The strategic distribution of mast cells closely reflects the primary role of these cells in providing first-line defense against environmental dangers, in regulating local and systemic inflammatory reactions and in shaping innate and adaptive immune responses. Human mast cells have pleiotropic and multivalent functions that make them highly versatile cells able to rapidly adapt responses to microenvironmental changes. They express a wide variety of surface receptors including immunoglobulin receptors, pathogen-associated molecular pattern receptors and danger signal receptors. The abundance of these receptors makes mast cells unique and effective surveillance cells able to detect promptly aggression by viral, bacterial and parasitic agents. In addition, mast cells express multiple receptors for cytokines and chemokines that confer them the capacity of being recruited and activated at sites of inflammation. Once activated by immunological or nonimmunological stimuli mast cells secrete a wide spectrum of preformed (early) and de novo synthesized (late) mediators. Preformed mediators are stored within granules and are rapidly released in the extracellular environment to provide a fast vascular response that promotes inflammation and local recruitment of other innate immunity cells such as neutrophils, eosinophils, basophils and monocyte/macrophages. Later on, delayed release of multiple cytokines and chemokines from mast cells further induce modulation of cells of adaptive immunity and regulates tissue injury and, eventually, resolution of inflammation. Finally, mast cells express several costimulatory and inhibitory surface molecules that can finely tune activities of T cells, B cells and regulatory cells by cognate interactions within lymphoid organs. The multivalent capacity to recognize and to react to internal and external dangers together with their ability to cross-talk with other immunocompetent cells make mast cells a unique effector cell of innate responses and a main bridge between innate and adaptive immunity.

A New Class of Meromorphic Multivalent Functions Defined by Linear Operator

A New Class of Meromorphic Multivalent Functions Defined by Linear Operator

On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator

The purpose of this paper is to introduce subclasses of multivalent functions by using linear operator defined by generalized fractional differintegral operator. We investigate various properties for functions of these subclasses.

Argument inequalities of certain subclass of multivalent functions defined by using new integral operator

In this paper, we introduce some interesting inequalities regarding the argument of certain p-valent functions. The subclass under investigation is defined by using certain new integral operator. Moreover, special cases and connections of the results presented here with those obtained in earlier works are pointed out.

Certain subclasses of meromorphic p-valent functions involving the El-Ashwah operator

In this paper, we introduce and investigate some inclusion theorems, convolution theorems and class preserving transforms for subclasses of the meromorphic multivalent function associated with the El-Ashwah operator. Some interesting corollaries and consequences of the main results are pointed out.

Defining the multivalent functions of CTCF from chromatin state and three-dimensional chromatin interactions.

CCCTC-binding factor (CTCF) is a multi-functional protein that is assigned various, even contradictory roles in the genome. High-throughput sequencing-based technologies such as ChIP-seq and Hi-C provided us the opportunity to assess the multivalent functions of CTCF in the human genome. The location of CTCF-binding sites with respect to genomic features provides insights into the possible roles of this protein. Here we present the first genome-wide survey and characterization of three important functions of CTCF: enhancer insulator, chromatin barrier and enhancer linker. We developed a novel computational framework to discover the multivalent functions of CTCF based on chromatin state and three-dimensional chromatin architecture. We applied our method to five human cell lines and identified ∼46 000 non-redundant CTCF sites related to the three functions. Disparate effects of these functions on gene expression were found and distinct genomic features of these CTCF sites were characterized in GM12878 cells. Finally, we investigated the cell-type specificities of CTCF sites related to these functions across five cell types. Our study provides new insights into the multivalent functions of CTCF in the human genome.

An improvement of Ozaki’s P-valent conditions

The old result due to [Ozaki, S.: On the theory of multivalent functions II. Sci. Rep. Tokyo Bunrika Daigaku Sect. A, 45–87 (1941)], says that if \(f\left( z \right) = {z^p} + \sum\nolimits_{n = p + 1}^\infty {{a_n}} {z^n}\) anzn is analytic in a convex domain D and for some real α we have Re{exp(iα)f(p)(z) >} 0 in D, then f(z) is at most p-valent in D. In this paper, we consider similar problems in the unit disc D = {z ∈ C: |z| < 1}.

On some interesting properties for a new subclass of multivalent functions

In this paper, we establish a new subfamily [Formula: see text] of multivalent functions with negative coefficients that involve certain linear operator. We first investigate sharp results concerning coefficients, then obtain the distortion theorem, radius of convexity and close-to-convexity, closure theorem, neighborhood property, partial sums and integral representation.