The Study of KKM Theorems With Applications to Vector Equilibrium Problems and Implict Vector Variational Inequalities Problems

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

“…Remark 1. In the particular case X = Z, P = 1 X and ρ is either ρ 1 or ρ 2 the previous theorem generalizes Theorems 2.5 and 2.6 in [17], 3.1 and 3.5 in [18], and 3.1 in [20]. In the above mentioned results Y is a convex set in a topological vector space and T ∈ KKM (Y, X).…”

“…The concepts introduced below extend to G-convex spaces the corresponding notions from vector spaces (see [18]). Definition 2.…”

Existence of solutions for generalized vector quasi-equilibrium problems

“…Then we give two examples to explain that our existence results with the compact assumption of E are different from corresponding results in [15,16,19]. We also illustrate that our existence result without the compact assumption of E is a generalization of the corresponding one in [13].…”

“…Another technique is well-known KKM theorems or fixed pointed theorems which have been used to study the existence results of various classes of equilibrium problems for the past years. For the details, we can refer to [10][11][12][13][14][15][16][17][18][19][20] and the references therein.…”

“…In [13], applying the Fan-KKM theorem Lin and Chen investigated the special cases of (GVQEP2) and (GVQEP3) when S(x) = E. In [16] Ansari and Flores-Bazan studied a special case of (GVQEP1) when T (x) is singleton. By using the fixed point theorem in [14] and maximal element theorem in [22], they obtained some existence results under conditions with or without involving φ-condensing maps.…”