The class of functions spirallike with respect to a boundary point.
The class of functions convex in the negative direction of the imaginary axis of order .
On the class of functions strongly starlike of order α with respect to a point
We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).
On coefficient inequalities in the Carathéodory class of functions
Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.
Some subclasses of close-to-convex functions
For α ∈ [0,1] and β ∈ (-π/2,π/2) we introduce the classes defined as follows: a function f regular in U = z: |z| < 1 of the form , z ∈ U, belongs to the class if for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in are examined.
Strongly starlike and spirallike functions
The aim of this paper is to present a new method of proof of an analytic characterization of strongly starlike functions of order (α,β). The relation between strong starlikeness and spirallikeness of the same order is discussed in detail. Some well known results are reproved.
Boundary subordination
We study the idea of the boundary subordination of two analytic functions. Some basic properties of the boundary subordination are discussed. Applications to classes of univalent functions referring to a boundary point are demonstrated.
On the class of functions defined in a halfplane and starlike with respect to the boundary point
The purpose of this paper is to study the class of univalent analytic functions defined in the right halfplane ℍ and starlike w.r.t. the boundary point at infinity. An analytic characterization of functions in is presented.
Differential subordinations for fractional-linear transformations.
Page 1