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.
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Acknowledgements
This work was supported by the strategic grant POSDRU/89/1.5/S/58852, Project called “Postdoctoral programme for training scientific researchers”, cofinanced by the European Social Found within the Sectorial Operational Program Human Resources Development 2007-2013.
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Communicated by Antonino Maugeri.
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Patriche, M. Fixed Point and Equilibrium Theorems in a Generalized Convexity Framework. J Optim Theory Appl 156, 701–715 (2013). https://doi.org/10.1007/s10957-012-0133-3
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DOI: https://doi.org/10.1007/s10957-012-0133-3