On differential subordinations for a class of analytic functions defined by a linear operator.
On Dyakonov type theorems for harmonic quasiregular mappings
We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.
On Extreme Points of Families of Analytic Functions with Values in a Convex Set.
On one application of differential subordinations
On some results for -spirallike functions of complex order of higher-order derivatives of multivalent functions.
On starlikeness of certain integral transforms
Let A denote the class of normalized analytic functions in the unit disc U = z: |z| < 1. The author obtains fixed values of δ and ϱ (δ ≈ 0.308390864..., ϱ ≈ 0.0903572...) such that the integral transforms F and G defined by and are starlike (univalent) in U, whenever f ∈ A and g ∈ A satisfy Ref’(z) > -δ and Re g’(z) > -ϱ respectively in U.
On subordination and superordination of new multiplier transformation.
On subordination of certain subclass of analytic functions.
On the Behavior of Holomorphic Functions Near Maximum Modulus Sets.
On the extreme points of subordination families
We investigate extreme points of some classes of analytic functions defined by subordination and classes of functions with varying argument of coefficients. By using extreme point theory we obtain coefficient estimates and distortion theorems in these classes of functions. Some integral mean inequalities are also pointed out.
On the Iversen-Tsuji theorem quasiregular mappings.
On the Phragmén-Lindelöf principle for a polyangle
On the sharp constant for starlikeness.
On the Size of Balls Covered by Analytic Transformations.
On the unified class of functions of complex order involving Dziok-Srivastava operator.
Phragmén-Lindelöf theorems for subharmonic functions on the unit disk.
Quasiregular mappings of maximal local modulus of continuity.
Region of variability for functions with positive real part
For γ ∈ ℂ such that |γ| < π/2 and 0 ≤ β < 1, let denote the class of all analytic functions P in the unit disk with P(0) = 1 and in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability for when P ranges over the class As a consequence, we present the region of variability for some subclasses of univalent functions. We also graphically illustrate the region of variability for several sets of parameters.
Sampling Sets for the Nevanlinna class.
Sandwich-type results for a class of functions defined by a generalized differential operator