Certain New Classes of Analytic Functions with Varying Arguments

2011

In this paper, using the generalized Al-Oboudi operator we introduce the new subclass H μ λ (α, β) of analytic functions. We also consider the subclass H μ λ (α, β) of H μ λ (α, β). Coefficient inequalities and convolution conditions are investigated for these classes.

Certain classes of analytic functions are defined which will generalize new, as well as well-known, classes of k-uniformly convex and starlike functions. We provide necessary and sufficent coefficient conditions, distortion bounds, extreme points and radius of starlikeness for these classes.

In the present paper, we introduce and investigate some properties of two subclasses Λn(λ, β) and Λ + n (λ, β); meromorphic and starlike functions of order β. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.

Making use of Linear operator theory, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

2015

Let Fp(b,M) denote the class of functions f(z) = z + ∑∞ k=2 akz k which are analytic in the open unit disc U = {z : |z| < 1} and satisfy the inequality ∣∣∣∣∣∣∣ b− 1 + zf ′ (z) f(z) b −M ∣∣∣∣∣∣∣ < M for b 6= 0, complex,M > 1 2 , |a2| = 2p, 0 ≤ p ≤ ( 1 +m 2 ) |b| , m = 1− 1 M and for all z ∈ U. Further f(z) is in the class Gp(b,M) if zf ′ (z) is in the class Fp(b,M). In the present paper, we obtain lower bounds for the classes introduced above and apply them to determine γ-spiral radiu for functions of the class Fp(b,M) and γ-convex radius for functions of the class Gp(b,M). 2010 Mathematics Subject Classification. 30C45.

Acta Mathematica Scientia, 2011

In this paper we introduce new classes of analytic functions with fixed argument of coefficients defined by subordination. Coefficient estimates, distortion theorems, integral means inequalities, and the radii of convexity and starlikeness are investigated. Convolution properties are also pointed out.

Applied Mathematics Letters, 2011

We denote by A, the class of all analytic functions f in the unit disc ∆ = {z ∈ C : |z| < 1} with the normalization f (0) = f ′ (0) − 1 = 0. For a positive number λ > 0, we denote by U 3 (λ) the class of all f (z) = z + ∑ ∞ n=2 a n z n ∈ A, such that a 3 − a 2 2 = 0, and satisfying the condition       z f (z)  2 f ′ (z) − 1      < λ, z ∈ ∆. A function f ∈ A is said to be in SR(γ) if | arg f ′ (z)| < π γ /2. In this paper, we find conditions on λ, α and γ such that U 3 (λ) is included in the class of all starlike functions of order α, or the class of all strongly starlike functions of order γ , or SR(γ), respectively.

International Journal of Mathematics and Mathematical Sciences, 2011

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack&#39;s Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

2008

The main object of this paper is to derive the sufficient conditions for the function z{p q(z)} to be in the classes of uniformly starlike and uniformly convex functions. Similar results using integral operator are also obtained.

Mathematical and Computer Modelling, 2011

We investigate the new class H b (α, β) of analytic functions with Koebe type. The subordination, superordination, best dominant result for that class was obtain. And by making use of Jack's Lemma as well as several differential and other inequalities, the authors derive sufficient conditions for starlikeness of the class H b (α, β) of n-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in earlier works are also indicated.