Fixed Point and Equilibrium Theorems in a Generalized Convexity Framework
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. Kims new model.
fixed point \(\mathbb{b}\)-convexity quasi-equilibria set-valued maps with ?-weakly \(\mathbb{b}\)-convex graph ?-naturally \(\mathbb{b}\)-quasiconvex set-valued maps