A unified representation of some starlike and convex harmonic functions with negative coefficients

Uniformly Starlike and Convex Functions with Negative Coefficients

Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...

On Certain Multivalent Starlike or Convex Functions with Negative Coefficients

A Certain Subclass of Uniformly Convex and Starlike Functions with Negative Coefficients

By making use of the familiar Salagean derivatives, a systematic investigation of a certain subclass of uniformly convex and starlike functions with negative coefficients is presented. In addition to finding various coefficient bounds and a number of characterization and distortion theorems, a number of other potentially interesting properties of this class of functions are investigated. Finall...

Initial coefficients of starlike functions with real coefficients

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions

On a Subclass of Certain Starlike Functions with Negative Coefficients

A certain subclass TΩ(n, p, λ, α)of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class TΩ(n, p, λ, α). Coefficient inequalities, distortion theorems and closure theorems of functions belonging to the class TΩ(n, p, λ, α) are determined. Also we obtain radii of convexity for the class ...