Subordination by Univalent Functions

Subordination Properties for New Certain Subclasses of Univalent Functions

In this paper, we obtain some subordination results for certian subclasses of univalent functions defined by convolution.

Subordination by convex functions

Coefficient Estimates for a Subclass of Bi-univalent Functions Defined by Salagean Operator Using Quasi Subordination

In this present investigation, we consider the subclass of analytic and bi-univalent functions associated with salagean operator consisting of the function class Σ in the unit open disk, which satisfies the qusi-subordination conditions. Also we obtain the first two Taylor-Maclaurin coefficients for functions in this new subclass. Mathematics Subject Classification: 30C45, 30C50

Subclasses of Bi-Univalent Functions of Complex Order Based On Subordination Conditions Involving Wright Hypergeometric Functions

In this paper, we introduce and investigate a new subclass of biunivalent functions ∑ of complex order defined in the open unit disk, which are associated with hypergeometric functions and satisfy subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients 2 | | a and 3 | | a for functions in the new subclass. Several (known or new) consequences of the results ar...

Subordination by Convex Functions

Let K(α), 0≤α< 1, denote the class of functions g(z)= z+∑∞n=2anzn which are regular and univalently convex of order α in the unit disc U . Pursuing the problem initiated by Robinson in the present paper, among other things, we prove that if f is regular in U , f(0) = 0, and f(z)+zf ′(z) < g(z)+zg′(z) in U , then (i) f(z) < g(z) at least in |z| < r0, r0 = √ 5/3 = 0.745 . . . if f ∈ K; and (ii) f...