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The 2-sphere is Wecken for n-valued maps

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We prove the theorem of the title. Every n-valued map $$\phi :S^2 \multimap S^2$$ϕ:S2⊸S2 of the 2-sphere has the Wecken property for n-valued maps, that is, it is n-valued homotopic… Click to show full abstract

We prove the theorem of the title. Every n-valued map $$\phi :S^2 \multimap S^2$$ϕ:S2⊸S2 of the 2-sphere has the Wecken property for n-valued maps, that is, it is n-valued homotopic to a map with $$N(\phi )$$N(ϕ) fixed points, where $$N(\phi )$$N(ϕ) is the Nielsen number of $$\phi $$ϕ.

Keywords: valued maps; sphere wecken; wecken valued

Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2019

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