Wyniki wyszukiwania - BazTech

1

Open relations and collectionwise normality

Gutev V.

Bulletin of the Polish Academy of Sciences. Mathematics

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2017

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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.

2

Characterizations of some classes of perfect spaces in terms of continuous selections avoiding supporting sets

Yamauchi T.

Bulletin of the Polish Academy of Sciences. Mathematics

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2008

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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.

3

On minimax inequalities in topological spaces without convexity structure

Lu H.-S.

Journal of Applied Analysis

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2007

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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.

4

Error bounds for convex constrained systems in Banach spaces

Song W.

Control and Cybernetics

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2007

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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.

5

Fixed point theorem for sequences of maps

Türkoğlu D., Altun I., Fisher B.

Demonstratio Mathematica

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2005

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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.

6

Inversion of multifunctions and differential inclusions

Nachi K., Penot J.-P.

Control and Cybernetics

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2005

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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.

7

Selections of bounded variation

Chistyakov V. V.

Journal of Applied Analysis

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2004

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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.

8

Generalized vector quasi-variational inequalities

Song W.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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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.