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1
Content available remote The unit ball of Ls(2l3∞)
EN
We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space Ls(2l3∞).
EN
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.
EN
In this paper we introduce a unified representation of starlike and convex harmonic functions with negative coefficients, related to uniformly starlike and uniformly convex analytic functions. We obtain extreme points, distortion bounds, convolution conditions and convex combinations for this family.
EN
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.
EN
In this paper, we further investigate the class of functions (…) which are analytic in the open unit disk (…),and involve the combinations of the representations of p-valently starlike and convex functions. We obtain several generalized results on the modified-Hadamard product of the class (…) which extend the corresponding results obtained by Altintas et al. [Computers Math. Applic. 30(2), 9-16, (1995)]; Darwish, Aouf [Mathematical and Computer Modelling (2007), doi:10.1016/j.mcm.2007.08.016 ]. Futher, by fixing the second coefficient of functions in (…) we introduce the special class (…) and discuss the extreme points.
EN
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.
7
Content available remote Second-order viability problem: a baire category approach
EN
The paper deals with the existence of viable solutions to the differential inclusion x(t) ∈ ƒ(t, x(t)) + ext F(t, x(t)), where ƒ is a single-valued map and ext F(t, x) stands for the extreme points of a continuous, convex and noncompact set-valued mapping F with nonempty interior.
EN
Making use of Dziok-Srivastava operator we introduced a new class of complex-valued harmonie functions which are orientation preserving, univalent and starlike with respect to other points. We investigate the coefficient bounds.distortion inequalities, extreme points and inclusion results for the generalized class of functions.
9
Content available remote On a subclass of p-valent functions
EN
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.
10
Content available remote Set-valued version of Sincov's functional equation
EN
We investigate selections of set-valued solutions of Sincov's functional equation that satisfy the same equation.
EN
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].
12
Content available remote Remark on the abstract Dirichlet problem for Baire-one functions
EN
We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function. We also study the analogous questions for functions of higher Baire classes.
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