KKM type theorems and generalized vector equilibrium problems in noncompact FC-spaces

Abstract

A new KKM type theorem is first proved under noncompact setting of FC-spaces. As applications of the KKM type theorem, we establish some new existence theorems of solutions for generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.

Weak-equilibrium problems in G-convex spaces

“…The results obtained in this section could be compared with closely related results such as Theorems 4.7-4.10 in [6], Theorems 3 and 5 in [11] and Theorems 4.11-4.14 in [15].…”

“…These problems, all or part of them, have been also studied in topological vector space by Fu and Wan [11] and Lin and Chen [15] and in F C spaces by X. P. Ding and T. M. Ding [6].…”

“…This problem includes fundamental mathematical problems like optimization problems, variational inequalities, fixed point problems, saddle point problems, problems of Nash equilibria, complementary problems (see [4]). In the last years the scalar equilibrium problem was extensively generalized in several ways to vector equilibrium for multivalued mappings (see [1], [2], [5][6][7][8][9][10][11], [13][14][15][16][17][18] and the references therein).…”

Coincidence theorems and minimax inequalities in abstract convex spaces

“…All conditions of Theorem 3.6 are satisfied for D instead of Y and for Y instead of Z, where s is the identity map on D. Therefore, one can deduce that [26] and [27], without the assumption "compactly" in FC-spaces and Corollary 3.1 [29] in abstract convex minimal spaces. 4) The compactness condition of multimap T in Theorem 3.5 and Theorem 3.6 can be replaced by the coercivity condition (see [24]) in minimal spaces.…”

Inclusion and Intersection Theorems With Applications in Equilibrium Theory in G-Convex Spaces

“…In many recent papers (see [1], [2], [4], [8]- [10], [12], [13], [15], [17]- [21], [29]) and the references therein) one studies one of more of the following equilibrium problems:…”