Fixed Point and Equilibrium Theorems in a Generalized Convexity Framework

Monica Patriche ()
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Monica Patriche: University of Bucharest

Journal of Optimization Theory and Applications, 2013, vol. 156, issue 3, No 9, 715 pages

Abstract: Abstract We study the fixed point property of set-valued maps and the existence of equilibria in the framework of $\mathbb{B}$ -convexity, recently defined by W. Briec and Ch. Horvath. We introduce some classes of the set-valued maps with generalized convexity and prove continuous selection and fixed point properties for them. Finally, we obtain results concerning the existence of quasi-equilibria for W.K. Kim’s new model.

Keywords: Fixed point; Quasi-equilibria; $\mathbb{B}$ -Convexity; Set-valued maps with ∗-weakly $\mathbb{B}$ -convex graph; ∗-Naturally $\mathbb{B}$ -quasiconvex set-valued maps (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0133-3

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