Search results for: Mirosław Ślosarski

Items from 1 to 16 out of 16 results

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Metrizable space of multivalued maps

Mirosław Ślosarski

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2021 > 20 > 77-93

In this article we define a metrizable space of multivalued maps. We show that the metric defined in this space is closely related to the homotopy of multivalued maps. Moreover, we study properties of this space and give a few practical applications of the new metric.

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Multi-invertible maps and their applications

Mirosław Ślosarski

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2019 > 18 > 35-52

In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of r-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.

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The properties and applications of relative homotopy

Mirosław Ślosarski

Topology and its Applications > 2016 > 210 > C > 183-200

In the article we have introduced a notion of relative homotopy. Thus we have recalled a notion of relative retract and relative extension of continuous maps. We have studied some properties of a relative homotopy and we have proven that it is an equivalence relation. We have defined the notion of relative contractibility and we have proven the theorem on the extension of a relative homotopy. We have...

article

The properties and applications of relative retracts

Mirosław Ślosarski

Journal of Fixed Point Theory and Applications > 2016 > 18 > 4 > 801-822

In this paper, we present relative retracts and we can say that these are multilevel retracts which either retain given properties depending on the level or not. Some properties are constant and are present on every level. These properties are especially important in regard to the theory of coincidence. The class of relative retracts consists of retracts in the sense of Borsuk, multiretracts and many...

article

The multi-morphisms and their properties and applications

Mirosław Ślosarski

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2015 > 14

In this paper a new class of multi-valued mappings (multi-morphisms) is defined as a version of a strongly admissible mapping, and its properties and applications are presented.

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Multidomination of metric spaces in the context of multimorphisms

Mirosław Ślosarski

Journal of Fixed Point Theory and Applications > 2015 > 17 > 4 > 641-657

The application of the theory of multimorphisms leads to the presentation of a new definition of a multidomination of metric spaces. With the help of this definition we obtain the new properties of multidomination in regard to multicontractibility, path connectedness and locally path connectedness.

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The properties of the multi-valued domination of metric spaces

Mirosław Ślosarski

Topology and its Applications > 2013 > 160 > 5 > 730-738

In this paper the properties of the multi-valued domination of metric spaces are presented, which allows to observe interesting relationships and similarities between absolute neighborhood multi-retracts (absolute multi-retracts) and absolute neighborhood retracts (absolute retracts).

article

The homotopies of admissible multivalued mappings

Mirosław Ślosarski

Open Mathematics > 2012 > 10 > 6 > 2187-2199

Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.

article

The homotopies of admissible multivalued mappings

Mirosław Ślosarski

Central European Journal of Mathematics > 2012 > 10 > 6 > 2187-2199

Certain properties of homotopies of admissible multivalued mappings shall be presented, along with their applications as the tool for examining the acyclicity of a space.

article

The multi-valued domination of metric spaces

Mirosław Ślosarski

Fixed Point Theory and Applications > 2012 > 2012 > 1 > 1-9

In this article, we introduce the notion of multi-valued domination of metric spaces, which is a generalization of domination in the sense of Borsuk and which encompasses previous generalizations. AMS classification: 32A12; 47H10; 55M20; 54C55; 54C15.

article

Locally admissible multi-valued maps

Mirosław Ślosarski

Discussiones Mathematicae, Differential Inclusions, Control and Optimization > 2011 > 31 > 1 > 115-132

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.

article

Generalized Lefschetz Sets

Mirosław Ślosarski

Fixed Point Theory and Applications > 2011 > 2011 > 1 > 1-11

We generalize and modify Lefschetz sets defined in 1976 by L. Górniewicz, which leads to more general results in fixed point theory.

article

On a generalization of absolute neighborhood retracts

Robert Skiba, Mirosław Ślosarski

Topology and its Applications > 2009 > 156 > 4 > 697-709

In this paper we generalize the concept of absolute neighborhood retract by introducing the notion of absolute neighborhood multi-retract. Furthermore, the Lefschetz fixed point theorem for admissible maps defined on absolute neighborhood multi-retracts is proved.

article

Generalized Topological Essentiality and Coincidence Points of Multivalued Maps

Grzegorz Gabor, Lech Górniewicz, Mirosław Ślosarski

Set-Valued and Variational Analysis > 2009 > 17 > 1 > 1-19

A concept of generalized topological essentiality for a large class of multivalued maps in topological vector Klee admissible spaces is presented. Some direct applications to differential equations are discussed. Using the inverse systems approach the coincidence point sets of limit maps are examined. The main motivation as well as main aim of this note is a study of fixed points of multivalued maps...

article

Fixed points of mapping in Klee admissible spaces

Lech Górniewicz, Mirosław Ślosarski

Control and Cybernetics > 2007 > 36 > 3 > 825-832

article

Once More on the Lefschetz Fixed Point Theorem

Lech Górniewicz, Mirosław Ślosarski

Bulletin of the Polish Academy of Sciences. Mathematics > 2007 > 55 > 2 > 161-170

An abstract version of the Lefschetz fixed point theorem is presented. Then several generalizations of the classical Lefschetz fixed point theorem are obtained.

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