Approximate Fixed Point Theorems in Banach Spaces

Afif Ben Amar and Donal O’Regan
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Afif Ben Amar: University of Sfax, Faculty of Sciences, Department of Mathematics
Donal O’Regan: National University of Ireland, Galway, School of Mathematics

Chapter Chapter 7 in Topological Fixed Point Theory for Singlevalued and Multivalued Mappings and Applications, 2016, pp 173-186 from Springer

Abstract: Abstract Let Ω $$\Omega $$ be a nonempty convex subset of a topological vector space X. An approximate fixed point sequence for a map F : Ω → Ω ¯ $$F: \Omega \longrightarrow \overline{\Omega }$$ is a sequence { x n } n ∈ Ω $$\{x_{n}\}_{n} \in \Omega $$ so that x n − F ( x n ) → θ $$x_{n} - F(x_{n})\longrightarrow \theta$$ . Similarly, we can define approximate fixed point nets for F. Let us mention that F has an approximate fixed point net if and only if θ ∈ { x − F ( x ) : x ∈ Ω } ¯ . $$\displaystyle{\theta \in \overline{\{x - F(x): x \in \Omega \}}.}$$

Keywords: Nash Equilibrium; Fixed Point Theorem; Topological Vector Space; Strategy Space; Reflexive Banach Space (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-31948-3_7

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