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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Displaying similar documents to “A fixed point theorem for a class of multi-valued continuously differentiable maps”
On single-valuedness of set-valued maps satisfying linear inclusions.
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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...