On single-valuedness of set-valued maps satisfying linear inclusions.
Nikodem, Kazimierz, Popa, Dorian (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Nikodem, Kazimierz, Popa, Dorian (2008)
Banach Journal of Mathematical Analysis [electronic only]
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O'Regan, D. (1999)
Zeitschrift für Analysis und ihre Anwendungen
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Jesús Araujo, Krzysztof Jarosz (2003)
Studia Mathematica
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We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.
Gilles Fournier, Donald Violette (1987)
Annales Polonici Mathematici
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Merentes, N., Nikodem, K., Rivas, S. (1997)
Journal of Applied Analysis
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Grzegorz Gabor (1995)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Introduction Many authors have developed the topological degree theory and the fixed point theory for set-valued maps using homological techniques (see for example [19, 28, 27, 16]). Lately, an elementary technique of single-valued approximation (on the graph) (see [11, 1, 13, 5, 9, 2, 6, 7]) has been used in constructing the fixed point index for set-valued maps with compact values (see [21, 20, 4]). In [20, 4] authors consider set-valued...
J. Bryszewski, Lech Górniewicz (1976)
Fundamenta Mathematicae
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Lj. B. Ćirić (1972)
Matematički Vesnik
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Gilles Fournier, Lech Górniewicz (1976)
Fundamenta Mathematicae
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Robert F. Brown (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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A multifunction ϕ: X ⊸ Y is n-valued if ϕ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps ϕ: S¹ ⊸ S¹ are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(ϕ) of an n-valued ϕ: S¹ ⊸ S¹ of degree d equals |n - d| and ϕ is homotopic to an n-valued power map that has exactly |n - d| fixed points. Thus the Wecken property, that Schirmer established...
Mirosław Ślosarski (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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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.
Charles J. Himmelberg, F. S. Van Vleck (1976)
Mathematica Slovaca
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S. Patnaik (1969)
Fundamenta Mathematicae
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