Radii Of Convexity For Functions Research Articles

A subclass of harmonic univalent functions with positive coefficients associated with fractional calculus operator

In the present paper, we are defining a subclass of harmonic univalent functions with positive coefficients in unit disc $U$ by using fractional calculus operator. Further we obtain distortion bounds, extreme points and radii of convexity for functions belonging to this class and discuss a class preserving integral operator. Here we also determine that the class studied in this paper is closed under convolution and convex combinations.

A subclass of harmonic univalent functions with positive coefficients

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disc $U$ can be written in the form $f=h+\bar g$, where $h$ and $g$ are analytic in $U$. In this paper authors introduce the class, $R_H(\beta)$, $(1<\beta \le 2)$ consisting of harmonic univalent functions $f=h+\bar g$, where $h$ and $g$ are of the form $ h(z)=z+ \sum_{k=2}^\infty |a_k|z^k $ and $ g(z)= \sum_{k=1}^\infty |b_k| z^k $ for which $\Re\{h'(z)+g'(z)\}<\beta$. We obtain distortion bounds extreme points and radii of convexity for functions belonging to this class and discuss a class preserving integral operator. We also show that class studied in this paper is closed under convolution and convex combinations.

Certain subclasses of p-valent starlike functions defined by using a differential operator

The object of this paper is to introduce two interesting subclasses T n ∗ ( p , q , α , β , γ ) and C n ( p , q , α , β , γ ) of p-valent starlike functions defined by using a differential operator. We obtain coefficient estimates and distortion theorems for functions belonging to these classes. The radii of convexity for functions belonging to these classes are also determined. Finally, several applications involving an integral operator and certain fractional calculus operator are also considered.

A class of meromorphic univalent functions with positive and fixed finitely many coefficients

The object of the present paper is to derive several interesting properties of the class Lp, ck (a, Ş, y) consisting of regular and univalent meromorphic functions with positive and fixed finitely many coefficients. These incinde coefficient estimates, closure theorems, and radius of convexity for functions belonging to the class Sp, ck (a, P.Y).

Certain subclasses of starlike functions, I

The object of the present paper is to introduce two interesting subclasses J ∗(α, β, γ) and b (α, β, γ) of starlike functions in the open unit disk U , and prove various coefficient inequalities and distortion theorems for functions belonging to these subclasses. The radii of convexity for functions belonging to the classes J ∗(α, β, γ) and b (α, β, γ) are also determined.

A variational method for functions of bounded boundary rotation

Let f be a function analytic in the unit disc, properly normalized, with bounded boundary rotation. There exists a Stieltjes integral representation for 1 + zf(z)/f'(z). From this representation, and in view of a known variational formula for functions of positive real part, a variational formula is derived for functions of the form q(z) =1 + zf(z)/f'(z). This formula is for functions of arbitrary boundary rotation and does not assume the functions to be univalent. A new proof for the radius of convexity for functions of bounded boundary rotation is given. The extremal function for Re {F(f'(z))} is derived. Examples of univalent functions with arbitrary boundary rotation are given and estimates for the radius in which Re {f'(z)} > 0 are computed. The coefficient problem is solved for a4 for all values of the boundary rotation and without the assumption of univalency.