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1
Content available remote Extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm
Boulahia Fatiha, Hassaine Slimane
Opuscula Mathematica
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2021
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Vol. 41, no. 5
629--648
EN
In the present paper, we give criteria for the existence of extreme points of the Besicovitch-Orlicz space of almost periodic functions equipped with Orlicz norm. Some properties of the set of attainable points of the Amemiya norm in this space are also discussed.
2
Content available remote The unit ball of Ls(2l3∞)
Kim S. G.
Commentationes Mathematicae
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2017
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Vol 57, No. 1
1--7
EN
We classify the extreme and exposed symmetric bilinear forms of the unit ball of the space Ls(2l3∞).
3
On Janowski harmonic functions
Dziok J.
Journal of Applied Analysis
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2015
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Vol. 21, nr 2
99--107
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.
4
Content available A unified representation of some starlike and convex harmonic functions with negative coefficients
El-Ashwah R. M., Aouf M. K., Hassan A. A. M., Hassan A. H.
Opuscula Mathematica
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2013
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Vol. 33, no. 2
273--281
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.
5
Content available remote Extreme points and support points of a class of analytic functions with missing coefficients
Xiong L., Tian L, Luo S., Liu X.
Demonstratio Mathematica
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2013
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Vol. 46, nr 3
525--532
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.
6
Content available remote Some general results and extreme points of p-valent functions with negative coefficients
Xiong L.
Demonstratio Mathematica
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2011
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Vol. 44, nr 2
261-272
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.
7
Remarks on the spectrum of a compact convex set of compact operators
Pham K. A., Nguyen X. T.
Journal of Applied Analysis
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2010
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Vol. 16, nr 2
259-264
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.
8
Content available remote Second-order viability problem: a baire category approach
Aitalioubrahim M., Sajid S.
Bulletin of the Polish Academy of Sciences. Mathematics
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2009
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Vol. 57, no 1
9-23
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.
9
Content available remote A class of harminic starlike functions with respect to other points defined by Dziok-Srivastava operator
Murugusundaramoorthy G., Vijaya K., Auof M. K.
Journal of Mathematics and Applications
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2008
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Vol. 30
113-124
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.
10
Content available remote On a subclass of p-valent functions
Dziok J.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
63-71
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.
11
Content available remote Set-valued version of Sincov's functional equation
Smajdor W.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
101-105
EN
We investigate selections of set-valued solutions of Sincov's functional equation that satisfy the same equation.
12
Content available remote On some coefficient conditions for complex harmonic mappings with a pole at the infinity
Sibelska A.
Demonstratio Mathematica
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2006
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Vol. 39, nr 2
335-346
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].
13
Content available remote Remark on the abstract Dirichlet problem for Baire-one functions
Kalenda O. F. K.
Bulletin of the Polish Academy of Sciences. Mathematics
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2005
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Vol. 53, no 1
55-73
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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