New generalization of the existence of equilibrium for generalized game in abstract convex space (Q2823172)

First of all, two fixed point theorems are proved for set-valued mappings in noncompact abstract convex spaces in the sense of \textit{S. Park} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 4, 1028--1042 (2010; Zbl 1214.47042)]. Then, new notions of \(\mathcal U_A\)-mapping and \(\mathcal U_A\)-majorized mapping on the mentioned type of spaces are introduced and two existence results for maximal elements of such mappings are proved. Finally, the obtained results are used for proving existence theorems of the equilibrium of qualitative games and noncompact generalized games.