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 $𝔹$ ‐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.