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Session 35. Topological fixed point theory and related topics
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Applications of fixed point theorems in equilibrium problems |
Thaís Monis, Instituto de Geociências e Ciências Exatas, UNESP - Univ Estadual Paulista, Brazil
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The talk is based on the joint work with Professor Carlos Biasi
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Let \(X\) be a nonempty set and \(f : X \times X \to \mathbb{R}\) a real function such that \(f(x, x) = 0\), for all \(x \in X\).
The classical equilibrium problem (abbreviated, EP) consists of
finding \(\tilde{x} \in X\) such that \(f(\tilde{x}, x) \geq 0\) for every \(x \in X\). Our main goal is to show the existence of the weak local equilibrium via the Lefschetz fixed point theorem for admissible multivalued mappings.
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References- C. Biasi, T. F. M. Monis, Coincidence theorems and its applications to equilibrium problems , Journal of Fixed Point Theory and its Applications 9, 2011,
327-337.
- C. Biasi, T. F. M. Monis, Weak local Nash equilibrium - part II , Zbìrnik prac Ìnstitutu Matematiki NAN Ukraini 6, 2013, 209-224.
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