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.
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.
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...
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...
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.
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).
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.
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.
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.
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...
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