Adam Lecko

Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector

Some general theorems on differential subordinations of some functionals connected with arithmetic and geometric means related to a sector are proved. These results unify a number of well known results concerning inclusion relation between the classes of analytic functions built with using arithmetic and geometric means.

The class of functions spirallike with respect to a boundary point

The aim of this paper is to present an analytic characterization of the class of functions δ-spirallike with respect to a boundary point. The method of proof is based on Julias lemma.

Subclasses of Typically-Real Functions Defined by Ruscheweyh Derivative

For each A > —1 let 7r(A) be the class of all functions / analytic in B = { z e C : z < 1} of the form f(z) = z + akZk, 2 é D , having real coefficients and satisfying the condition Re | ( l — z 2) i j i i i f l | > 0, where L denote the Ruscheweyh derivative. Some basic properties of functions in 7r(A) are presented.

The class of functions convex in the negative direction of the imaginary axis of order (α,β)

The aim of this paper is to present an analytic characterization of the class of functions convex in the negative direction of the imaginary axis of order (α,β). The method of the proof is based on Julias lemma.

DIFFERENTIAL SUBORDINATIONS FOR FRACTIONAL- LINEAR TRANSFORMATIONS

We establish that the differential subordinations of the forms p(z)+γzp� (z) ≺ h(A1 ,B 1; z) or p(z)+ γzp � (z)/p(z) ≺ h(A2 ,B 2; z) implies p(z) ≺ h(A, B; z), where γ ≥ 0 and h(A, B; z) = (1 + Az)/(1 + Bz) with −1 ≤ B