Approximation by Polynomials Subordinate to a Univalent Function

Test Starlike Functions for Approximation by Subordinate Polynomials

1 Presented by We construct a function f (z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f * λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample to a result of Greiner and Ruscheweyh.

Subclasses of Univalent Functions Subordinate to Convex Functions

In this paper, we define a new subclass Ao(A, B) of univalent functions and investigate several interesting characterization theorems involving a general class S" [A, B] of starlike functions

On Approximation to an Arbitrary Function of a Complex Variable by Polynomials* By

Certain Subclasses of Bi–univalent Functions Satisfying Subordinate Conditions

In this paper, we introduce and investigate each of the following subclasses: SΣ(λ ,γ ;φ), H S Σ(α), RΣ(η ,γ ;φ) and BΣ(μ ;φ) (0 λ 1; γ ∈ C {0}; α ∈ C; 0 η < 1; μ 0) of bi-univalent functions, φ is an analytic function with positive real part in the unit disk D, satisfying φ(0) = 1, φ ′(0) > 0, and φ(D) is symmetric with respect to the real axis. We obtain coefficient bounds involving the Taylo...

The Fekete-Szegö problem for a general class of bi-univalent functions satisfying subordinate conditions

In this work, we obtain the Fekete-Szegö inequalities for the class $P_{Sigma }left( lambda ,phi right) $ of bi-univalent functions. The results presented in this paper improve the recent work of Prema and Keerthi [11].