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.

Coefficient Estimates for a Subclass of Bi-univalent Strongly Quasi-starlike Functions

The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for functions in this new subclass are estimated.

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.

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.

THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.

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.

DIFFERENTIAL SUBORDINATIONS AND α-CONVEX FUNCTIONS

This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.

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.

On a Subordination Result of a Subclass of Analytic Functions

In this paper, we investigate a subordination property and the coefficient inequality for the class M(1, b), The lower bound is also provided for the real part of functions belonging to the class M(1, b).

Majorization Results and Coefficients Bounds for a Class of Univalent Functions Associated with Operator

In this paper we introduce a new general subclass n,G∑ a,λ(A, B, α) of univalent functions related the known integral operator and differential operator. Some majorization results for n,G∑ a,λ(A, B, 1) as well as the other functions are given. Furthermore, we find the coefficients bounds on |a_2| and |a_3| for functions in*n,G∑ a,λ(A_1, B_1, A_2, B_2, α_1, α_2), which is the bi-univalent functions defined by n,G ∑a,λ(A, B, α) and subordination. By giving specific values of the parameters of our main results, several(known or new) consequences of main results are also discussed.

ON PROPERTIES OF THE PROPER SUBCLASS OF A UNIVALENT FUNCTION

This paper discusses the function class Hβ(a) of the from f(z)=z+∑k=(n+1)^+∞, which satisfies the conditon Re[f'(Z)+βzf″(z)]＞a, (0≤a＜1) in |z|＜1, with its inclusion relation ,neighborhood properties and the deviation theorem ,convolution properties in the case when f(z) has negative coefficients.

SPIRALLIKENESS CONDITIONS FOR ANALYTIC FUNCTIONS

Let α，β，γ and p be real,|a|<π/2,β>0,0≤p<1,and let f(z) be analytic in |z|<1 with f(0)=f'(0)-1=0.

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

ON A CLASS OF ANALYTIC FUNCTIONS RELATED TO CONIC DOMAINS AND ASSOCIATED WITH CARLSON-SHAFFER OPERATOR

Making use of the Carlson-Shaffer convolution operator, we introduce and study a new class of analytic functions related to conic domains. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. We also show that this class is closed under convolution with a convex function. Some applications are also discussed.

A Subclass of Harmonic Functions Associated with Wright’s Hypergeometric Functions

We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.

On new classes of strongly Janowski type functions of complex order

We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.

A Certain Subclass of Analytic Functions

In the present paper, we introduce a class of analytic functions in the open unit disc by using the analytic function qα(z)=3/(3+(α-3)z-αz2), which was investigated by Sokó? [1]. We find some properties including the growth theorem or the coefficient problem of this class and we find some relation with this new class and the class of convex functions.

Inclusion and Argument Properties for Certain Subclasses of Analytic Functions Defined by Using on Extended Multiplier Transformations

Making use of a multiplier transformation, which is defined by means of the Hadamard product (or convolution), we introduce some new subclasses of analytic functions and investigate their inclusion relationships and argument properties.

New Criterion for Starlike Integral Operators

In this paper, we introduce new sufficient conditions for certain integral operators to be starlike and p-valently starlike in the open unit disk.

On Sufficient Conditions for p-valently Starlikeness

Let An(p)(p,n ∈ N = {1,2,3,...}) denote the class of functions of the form f(z) = zp +ap+nzp+n +...which are analytic in the unit disk E = {z:|z| < 1}.A function f(z) in A(p) is said to be in the class Sp(a,b) if it satisfies zf(z) pf(z) 1 + az 1 + bz for some a and b(-1 ≤ b < a ≤ 1).In this paper,using the method of differential subordinations,we give new criteria for f(z) to be in the classes Sp(a,b)(-1 ≤ b < a ≤ 1),that is,if f(z) ∈ A(p) satisfies f(z) = 0 in 0 < |z| < 1,f(z) = 0 when μ = 1,and zf(z) f(z) μ 1 + zff((zz)) + λzff(z(z))h(z),where h(z) = p1+μ(1 + λ) 11 ++ abzz 1+μ + pμ(1 + az)1-μ(1+bz)1+μ,λ≥-1,μ∈ {-1,0,1},then f(z) ∈ Sp(a,b).Our results improve or extend some results due to Owa,Nunokawa,Padmanabhan,Silverman,Obradovic,Yang and others[3-10].