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1
Content available Some remarks about K-continuity of K-superquadratic multifunctions
Troczka-Pawelec K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2018
|
Vol. 23
57--64
EN
Let X = (X, +) be an arbitrary topological group. The set-valued function F : X → n(Y ) is called K-superquadratic iff F(x + y) + F(x − y) ⊂ 2F(x) + 2F(y) + K, for all x, y ∈ X, where Y denotes a topological vector space and K is a cone. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to K-boundedness. The case where Y = RN will be considered separately.
2
Content available K-continuity problem of K-superquadratic set-valued functions
Troczka-Pawelec K.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
227--235
EN
In this paper we study K-superquadratic set-valued functions.We will present here some connections between K-boundedness of K-superquadratic set-valued functions and K-semicontinuity of multifunctions of this kind.
3
Content available K-continuity of K-subquadratic set-valued functions
Troczka-Pawelec K., Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2014
|
Vol. 19
237--244
EN
Let X = (X, +) be an arbitrary topological group. A set-valued function F : X → n(Y) is called K-subquadratic if 2F(s) + 2F(t) ⊂ F(s + t) + F(s - t) + K, for all s, t ϵ X, where Y denotes a topological vector space and where K is a cone in this space. In this paper the K-continuity problem of multifunctions of this kind will be considered with respect to weakly K-boundedness. The case where Y = R N will be considered separately.
4
Content available remote On rare s-precontinuity for multifunctions
Ekici E., Jafari S.
Demonstratio Mathematica
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2013
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Vol. 46, nr 2
395--403
EN
In this paper, we introduce and study the notions of upper and lower rarely s-precontinuous multifunctions which are a generalization of weakly s-precontinuous multifunctions due to Ekici and Park [3].
5
Content available remote On sup-measurability of multifunctions with some density properties
Kwiecińska G.
Demonstratio Mathematica
|
2012
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Vol. 45, nr 4
821-833
EN
The paper is concerned with sup measurability of a multifunction F defined on the product (…) of metric spaces with some differentiation bases. We introduce the lower (…) property and the upper (…) property of multifunction, where (…), and we prove sup measurabilty of F when it has the upper (…) property at (x, y) and F(x, ź) has the lower (…) property at y for every (…). Some application of this theorem to the existence of solutions of differential inclusions (…) is given.
6
Content available remote The Demyanov metric and measurable multifunctions
Leśniewski A.
Journal of Mathematics and Applications
|
2010
|
Vol. 33
61-65
EN
We present in this paper measurability multifunctions in the family of all convex, bounded sets which need not be closed. The Demyanov metric is discussed.
7
Content available remote On some forms of quasi-uniform convergence of transfinite sequence of multifunctions
Przemski M.
Commentationes Mathematicae
|
2010
|
Vol. 50, [Z] 1
3-21
EN
In this paper we introduce various forms of convergence of transfinite sequences of multifunctions with values in a quasi-uniform space. We also study some weak types of continuity for such multifunctions. Any such sequence of multifunctions generates the sequence of the sets of weak types of continuity points and the sequence of various types of cluster sets of members of such sequence. We study the connection between convergence of a transfinite sequences of multifunctions and convergence of the corresponding sequences of the sets of the weak continuity points and the sequences of cluster sets. Some of the presented results concern of general nets of multifunctions.
8
Content available On the continuity of the integrable multifunctions
Piątek B.
Opuscula Mathematica
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2009
|
Vol. 29, no. 1
81-88
EN
The generalization of the Polovinkin theorem is studied.
9
Content available remote On E-continuity and E-minimality of multifunctions of two variables
Strońska E.
Demonstratio Mathematica
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2009
|
Vol. 42, nr 1
47-52
EN
In this article we formulate and prove some sufficient conditions for the l-Ex xy-continuity and the Ex x y- minimality of multifunctions of two variables.
10
Content available remote Cluster sets and related properties of multifunctions
Przemski M.
Demonstratio Mathematica
|
2009
|
Vol. 42, nr 1
205-219
EN
In this paper we present some types of cluster sets of multifunction. Using these concepts we relate properties of cluster sets to some generalized continuity properties, minimality of multifunctions and closedness of its graphs.
11
Content available remote Representing a non-associated constitutive law by a bipotential issued from a Fitzpatrick sequence
Vallée C., Lerintiu C., Fortuné D., Atchonouglo K., Ban M.
Archives of Mechanics
|
2009
|
Vol. 61, nr 3-4
325-340
EN
We analyze the relation between Géry de Saxcé's bipotentials representing non-associated constitutive laws and Fitzpatrick's functions representing maximal monotone multifunctions. We illustrate by two examples (one linear and monotone, the other non-linear and non-monotone) the fact that Fitzpatrick's representation coming from convex analysis provides a constructive method to discover the "best" bipotential modelling of a given Implicit Standard Material.
12
Content available remote On the relationships between the graphs of multifunctions and some forms of continuity
Przemski M.
Demonstratio Mathematica
|
2008
|
Vol. 41, nr 1
203-224
EN
In this paper we continue the study of the concept of graph continuity. We extend to multifunctions some results on the relationships between the graphs of functions. In addition, we introduce some generalized forms of continuity for multifunctions.
13
On a Jansen type functional equation
Smajdor W.
Journal of Applied Analysis
|
2007
|
Vol. 13, nr 1
19-31
EN
We investigate the functional equation [wzór] for f: M S, where M is an Abelian 2- and 3-divisible group and S is an abstract convex cone. The motivation for studying this equation came from results due to Tiberiu Trief [8] and Young Whan Lee [3], where equation (1) was considered with constants a = 3, b = 2 and a = 9 and b = 4, respectively.
14
Content available remote Some properties of upper and lower θ-quasicontinuous multifunctions
Noiri T., Popa V.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 1
223--234
EN
In this paper we obtain new characterizations of upper and lower θ-quasicontinuous muitifunctions and investigate several properties of such multifunctions.
15
Content available remote Slightly beta-continuous multifunctions
Ekici E.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 2
469-484
EN
In this paper, we introduce and study upper and lower slightly beta-continuous multifunctions as a generalization of upper (lower) semicontinuous, upper (lower) alfa-continuous, upper (lower) precontinuous, upper (lower) quasi-continuous, upper (lower) gamma-continuous, upper (lower) beta-continuous multifunctions and slightly beta-continuous functions. Some characterizations and several properties concerning upper (lower) slightly beta-continuous multifunctions are obtained. Furthermore, the relationships between upper (lower) slightly beta-continuous multifunctions and other related multifunctions are also discussed.
16
Content available remote On the Sincov functional equation
Piątek B.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 4
875--881
EN
The Riemarm integral, the Hukuhara differences and derivatives will be applied to obtain solutions of the Sincov functional equation.
17
Content available remote On some approximation problems in Musielak-Orlicz spaces of multifunctions
Kasperski A.
Demonstratio Mathematica
|
2004
|
Vol. 37, nr 2
393--406
EN
We introduce the Musielak-Orlicz spaces of multifunctions Xmphi and Xc,m,phi. We prove that these spaces are complete. Also, we get some convergence and approximation theorems in these spaces.
18
Content available remote On weak compactness and lower closure results for Pettis integrable (multi) functions
Balder E. J., Sambucini A. R.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
|
Vol. 52, nr 1
53-61
EN
In [4, 5, 7] an abstract, versatile approach was given to sequential weak compactness and lower closure results for scalarly integrable functions and multifunctions. Its main tool is an abstract version of the Komlos theorem, which applies to scalarly integrable functions. Here it is shown that this same approach also applies to Pettis integrable multifunctions, because the abstract Komlos theorem can easily be extended so as to apply to generalized Pettis integrable functions. Some results in the literature are thus unified.
19
Content available Control problems for systems described by hemivariational inequalities
Denkowski Z.
Control and Cybernetics
|
2002
|
Vol. 31, no 3
713-738
EN
The paper considers some control problems for the systems described by the evolution, as well as the stationary hemivariational inequalities (HVIs for short). First, basing on surjectivity theorems for pseudo-monotone operators we formulate some existence results for the solutions of the HVIs and investigate some properties of the solution set (like sensitivity; i.e. its dependence on data and operators). Next we quote some existence theorems for optimal solutions for various classes of optimal control like distributed control (e.g. Bolza problem), identification of parameters, or optimal shape design for systems described by HVIs. Finally, we discuss some common features in getting the existence of optimal solutions as well as some "well-posedness" problems.
20
Content available remote On multidifferentials of multifunctions
Girejko E.
Zeszyty Naukowe Politechniki Białostockiej. Matematyka, Fizyka, Chemia
|
2001
|
Z. 20
23--35
EN
In this article some properties of multidiffereiitials of set-valued maps (multifunctions) are studied. The functions considered here are mostly those that are not differentiable in a classical sense. Existence of minimal multidifferentials has been proved.
PL
W artykule tym badane są pewne własności multiróżniczek funkcji wielo wartościowych (multifunkcji). Rozpatrywane funkcje nie są, zwykle różniczkowalne w klasycznym sensie. Pokazano istnienie minimalnych multiróżniczek.
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