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On Janowski harmonic functions

Dziok J.

Journal of Applied Analysis

2015

Vol. 21, nr 2

99--107

In this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.

Extreme points and support points of a class of analytic functions with missing coefficients

Xiong L., Tian L, Luo S., Liu X.

Demonstratio Mathematica

2013

Vol. 46, nr 3

525--532

Let Mn(a, b, c) denote a class of functions of the form (...) which are analytic in open unit disk (...) and satisfy the condition (...). In this paper, we obtain the extreme points and support points of the class Mn(a, b, c) of functions.

Remarks on the spectrum of a compact convex set of compact operators

Pham K. A., Nguyen X. T.

Journal of Applied Analysis

2010

Vol. 16, nr 2

259-264

In this note we derive a necessary and sufficient condition for a compact convex set of linear compact operators acting in a complex Hilbert space to have the spectrum outside a prescribed closed convex subset of the complex plane.

On a subclass of p-valent functions

Dziok J.

Demonstratio Mathematica

2008

Vol. 41, nr 1

63-71

In this paper we consider a subclass of p-valent functions defined by certain differential-integral operator. By using the Krein-Milman theorem we obtain the extreme points of the classs. Some extremal problems in the class are also determined.

On some coefficient conditions for complex harmonic mappings with a pole at the infinity

Sibelska A.

Demonstratio Mathematica

2006

Vol. 39, nr 2

335-346

In 1984 J. Clunie and T. Sheil-Small initiated studies of complex functions harmonic in the unit disc. In 1987 W. Hergartner and G. Schober considered mappings of this type, defined in the domain U = {z is an element of C : \z\ > 1}. Several mathematicians examine classes of complex harmonic functions with some coefficient conditions, defined in the unit disc (e.g. [2], [5], [10], [1] [9]) or in U (e.g. [8], [7]). We investigate the classes of mappings harmonic in U with coefficient conditions more general than the considered in paper [8].