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1
Content available remote Characterizations of some classes of perfect spaces in terms of continuous selections avoiding supporting sets
100%
Yamauchi T.
Bulletin of the Polish Academy of Sciences. Mathematics
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2008
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tom Vol. 56, no 2
149-161
EN
Some kinds of perfect spaces, including paracompact perfectly normal spaces and collectionwise normal perfect spaces, are characterized in terms of continuous selections avoiding supporting sets. A necessary and sufficient condition on a domain space for a selection theorem of E. Michael [Fund. Math. 47 (1959), 173-178] to hold is also obtained.
2
Content available Boundedness of set-valued stochastic integrals
100%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2015
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tom 35
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nr 2
197-207
EN
The paper deals with integrably boundedness of Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4], where has not been proved that this integral is integrably bounded. The problem of integrably boundedness of the above set-valued stochastic integrals has been considered in the paper [7] and the monograph [8], but the problem has not been solved there. The first positive results dealing with this problem due to M. Michta, who showed (see [11]) that there are bounded set-valued 𝔽-nonanticipative mappings having unbounded Itô set-valued stochastic integrals defined by E.J. Jung and J.H. Kim. The present paper contains some new conditions implying unboundedness of the above type set-valued stochastic integrals.
3
Content available remote Open relations and collectionwise normality
100%
Gutev V.
Bulletin of the Polish Academy of Sciences. Mathematics
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2017
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tom Vol. 65, no. 1
69--79
EN
Using the framework of discrete-valued relations, we give a simple proof of a theorem obtained by Stoyan Nedev. This theorem provides a generalisation of an element in the proof of Dowker’s extension theorem, which is essential for constructing continuous selections of set-valued mappings defined on collectionwise normal spaces. Using this relationship, we also give a simple proof of the Dowker’s theorem.
4
Content available remote Trivial bundles of spaces of probability measures and countable-dimensionality
88%
Gutev V. G.
Studia Mathematica
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1995
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tom 114
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nr 1
1-11
EN
The probability measure functor P carries open continuous mappings $f: X onto → Y$ of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers $f^{-1}(y)$ are infinite. This answers a question raised by V. Fedorchuk.
5
Content available remote Error bounds for convex constrained systems in Banach spaces
88%
Song W.
Control and Cybernetics
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2007
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tom Vol. 36, no 3
775-792
EN
In this paper, we first establish both primal (involving directional derivatives and tangent cones) and dual characterizations (involving subdifferential and normal cones) for the local (global) error bounds of constrained set-valued systems; as an application, we then derive both primal and dual characterizations for the local (global) error bounds of the constrained convex inequality systems in a general Banach space and also some sufficient conditions. The obtained results improve or generalize some known results.
6
Content available remote Fractals of generalized F− Hutchinson operator
88%
Nazir T. , Silvestrov S. , Abbas M.
|
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tom 2
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nr 1
EN
The aim of this paper is to construct a fractal with the help of a finite family of F− contraction mappings, a class of mappings more general than contraction mappings, defined on a complete metric space. Consequently, we obtain a variety of results for iterated function systems satisfying a different set of contractive conditions. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.
7
Content available remote Fixed point theorem for sequences of maps
75%
Türkoğlu D. , Altun I. , Fisher B.
Demonstratio Mathematica
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2005
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tom Vol. 38, nr 2
461--468
EN
In this paper, we prove a common fixed point theorem for sequences of maps under the condition of compatible mappings on complete metric space. We extend and generalize several fixed point theorems on complete metric space.
8
On minimax inequalities in topological spaces without convexity structure
75%
Lu H.-S.
Journal of Applied Analysis
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2007
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tom Vol. 13, nr 1
133-149
EN
In this paper, we give a new nonempty intersection theorem in general topological spaces without convexity structure. As its applications, some new minimax inequalities are obtained in general topological spaces without convexity structure.
9
Selections of bounded variation
63%
Chistyakov V. V.
Journal of Applied Analysis
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2004
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tom Vol. 10, nr 1
1-82
EN
The paper presents recent results concerning the problem of the existence of those selections, which preserve the properties of a given set-valued mapping of one real variable taking on compact values from a metric space. The properties considered are the boundedness of Jordan, essential or generalized variation, Lipschitz or absolute continuity. Selection theorems are obtained by virtue of a single compactness argument, which is the exact generalization of the Helly selection principle. For set-valued mappings with the above properties we obtain a Castaing-type representation and prove the existence of multivalued selections and selections which pass through the boundaries of the images of the set-valued mapping and which are nearest in variation to a given mapping. Multivalued Lipschitzian superposition operators acting on mappings of bounded generalized variation are characterized, and solutions of bounded generalized variation to functional inclusions and embeddings, including variable set-valued operators in the right hand side, are obtained. Bibliography contains 113 items.
10
Content available remote Generalized vector quasi-variational inequalities
51%
Song W.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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tom Vol. 46, no 4
401--417
EN
First we establish a general existence theorem for a generalized vector qusi-variational inequality in a topological vector space by using a set-valued and vector generalization of Ky Fan minimax principle. As applications, several existence theorems for generalized vector quasi-variational inequalities are derived under assumptions of order-lower (order-upper) semicontinuity or monotonicity of set-valued mappings.
11
Content available remote Inversion of multifunctions and differential inclusions
51%
Nachi K. , Penot J.-P.
Control and Cybernetics
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2005
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tom Vol. 34, no 3
871-901
EN
We present a new inverse mapping theorem for correspondences. It uses a notion of differentiability for multifunctions which seems to be new. We compare it with previous versions. We provide an application to differential inclusions.
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