On quasivariational inclusion problems of type I and related problems

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

“…These results improve and generalize the known results in [1] from compact convex subsets of locally convex topological vector spaces to noncompact locally F C-uniform spaces without convexity structure, from quasi-variational inclusion problems to systems of generalized vector quasi-variational inclusions, and from α quasi-optimization problems to a system of generalized vector α quasi-optimization problems. Some applications of our results are also discussed.…”

“…Let S : D × K → 2 D , T : D × K → 2 K , and F : K × D × D → 2 Z be set-valued mappings. Lin and Tan [1] studied the following problems:…”

“…These problems play a central role in vector optimization theory concerning set-valued mappings and have close relations with vector quasi-equilibrium problems, vector quasi-variational inequality problems, fixed point problems, quasi saddle problems, and minimax problems, for example, see [1][2][3][4][5][6][7][8] and the references therein. Lin and Tan [1] proved some existence results of solutions for these above problems under suitable assumptions. The purpose of this paper is to introduce and study new systems of generalized vector quasivariational inclusions and system of generalized vector α quasi-optimization problems in locally F C-uniform spaces without convexity structure.…”

“…If I is a singleton and C i (x) = C is a constant-valued closed convex cone in Z, then the SGVQVIP (I), SGVQVIP (II), and (SGVQOP) α reduce to the UQVIP (1), LQVIP (2), and (GVQOP) α (3) introduced by Lin and Tan [1] , respectively.…”

Some further applications of KKM theorem in topological semilattices

“…Definition 2.6. ( [8], Definition 2.2) Let X be a topological space, Y a topological vector space with a cone C. Given a subset D ⊂ X, we consider a multi-valued mapping F : D → 2 Y . The domain of F is defined to be the set domF = {x ∈ D : F (x) = ∅}.…”