ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS

In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.

Coefficient Estimates for Bi-Univalent Bazilevic Functions

In this paper we consider the class of Bazilevic functions for bi-univalent functions. For this we will estimate the coefficients a2 and a3 using Caratheodory func- tions and the method of differential subordination.

On the Coefficients of Several Classes of Bi-univalent Functions Defined by Convolution

In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.

Second Hankel Determinants and Fekete-Szegö Inequalities for Some Sub-Classes of Bi-Univalent Functions with Respect to Symmetric and Conjugate Points Related to a Shell Shaped Region

In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.

Coefficient Estimates for a Certain General Subclass of Analytic and Bi-Univalent Functions

Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass of analytic and bi-univalent functions defined in the open unit disc U. Further, we find estimates on the coefficients and for functions in this subclass. Many relevant connections with known or new results are pointed out.

Coefficient Estimates for a Class of m-fold Symmetric Bi-univalent Function Defined by Subordination

In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.

Fekete-Szegö Inequality for a Subclass of Bi-univalent Functions Associated with Hohlov Operator and Quasi-subordination

In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors.

Coefficient Estimates for Certain Subclasses of Bi-Univalent Ma-Minda Mocanu-Convex Functions

In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.

SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES

Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈C:|z|<1}, normalized by the conditions f(0) = 0 and f'(0) = 1. Let U denote the set of all functions f ∈ A satisfying the condition |(z/f(z))^2f'(z)-1|<1 for z∈D.Let Ω be the class of all f∈A for which |zf'(z)-f(z)|<1/2, z∈D.In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.

Univalent Criteria for Analytic Functions Involving Schwarzian Derivative

In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence criteria depending on parameters.Anal.Math.Phys.,2014,4(1-2):23–34)is generalized.

ON UNIVALENT BLOCH FUNCTIONS

A new characterization of univalent Bloch functions is given by investigating the growth order of an essentially increasing function. Our contribution can be considered as a slight improvement of the well-known Pommerenke's result and its all generalizations, and the proof presented in this paper is independently developed.

Integral Means of Univalent Solution for Fractional Differential Equation

By employing the Srivastava-Owa fractional operators, we consider a class of fractional differential equation in the unit disk. The existence of the univalent solution is founded by using the Schauder fixed point theorem while the uniqueness is obtained by using the Banach fixed point theorem. Moreover, the integral mean of these solutions is studied by applying the concept of the subordination.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

Faber polynomials with applications to univalent functions with quasiconformal extensions

We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.

Notes on Univalent Functions with Quasiconforml Extensions

We make improvements to some of the constants concerned with univalent functions with quasiconformal extensions that have appeared in the literature.

Univalent Functions and Diff(S^1)/S^1

The relation between Diff（S^1）/S^1 and the space of univalent analytic functions on the disk is elucidated and shown to provide upper bounds for the volumes of exhaustive approximations to an analytic submanifold of an infinite-dimensional space. The maximum magnitudes of the coefficients in the series expansions of univalent superanalytic functions on the superdisk are inferred.

Meiotic Behavior of 1BL/1RS Translocation Chromosome and Alien Chromosome in Two Tri-genera Hybrids

The behavior of wheat-rye translocation chromosome and alien chromosome including Thinopyrum and Haynaldia chromosome at meiosis was investigated in two hybrids by fluorescence in situ hybridization (FISH). Misdivision of translocation chromosome at anaphase I and rye chromatin micronucleus at tetrad stage were observed, A plant with one normal 1BL/1RS translocation chromosome and one 1BL/1RS translocation chromosome deleted about 1/3 of rye chromosome arm in length was identified. One plant with wheat-Thinopyrum non-Robertson translocation chromosome was also detected in the F-2 population of Yi4212 x Yi4095. That could be the results of unequal misdivision of wheat-rye 1BL/1RS translocation chromosome and Thinopyrum chromosome during meiosis. No interaction between translocation chromosome and alien chromosome at meiosis was supported by the data of the distribution frequencies of translocation chromosome and Thinopyrum or Haynaldia chromosome in the progeny of two hybrids. The results may be useful to cultivate new germplasms with different length of rye 1R short arm and wheat-alien non-Robertson translocation tines under wheat background.

Some Properties of Two Class of Analytic Functions Family

Let A be the class of functions f(z)=z+sum from n=2 to ∞ (a_nZ^n) which are analytic in the unit disc, and let In this paper, Some properties of Q_α(β) and R_α(β) are investigated. In particular, Some results due to chichra [4], Mocanu[5] and Obradovic[6] are extended. In addition, We also showed an error of S. Owa[8].