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We discuss the minimax problems for set-valued mappings with several hierarchical structures, and scalar hierarchical minimax theorems, hierarchical minimax theorems, hierarchical minimax inequalities for set-valued mappings, and the existence of cone-saddle points. [ABSTRACT FROM AUTHOR]

We study the minimax inequalities for set-valued mappings with hierarchical process and propose two versions of minimax inequalities in topological vector spaces settings. As applications, we discuss the existent results of solutions for set equilibrium problems. Some examples are given to illustrate the established results. [ABSTRACT FROM AUTHOR]

We study the well-posedness for generalized set equilibrium problems (GSEP) and propose two types of the well-posed concepts for these problems in topological vector space settings. These kinds of well-posedness arise from some well-posedness in the vector settings. We also study the relationship between these well-posedness concepts and present several criteria for the well-posedness of GSEP. Our results are new or include as special cases recent existing results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the minimax theorems for set-valued mappings with or without linear structure. We define several kinds of cone-convexities for set-valued mappings, give some examples of such set-valued mappings, and study the relationships among these cone-convexities. By using our minimax theorems, we derive some existence results for saddle points of set-valued mappings. Some examples to illustrate our results are also given. [ABSTRACT FROM AUTHOR]

We study the weak solutions and strong solutions of set equilibrium problems in real Hausdorff topological vector space settings. Several new results of existence for theweak solutions and strong solutions of set equilibrium problems are derived. The new results extend and modify various existence theorems for similar problems. [ABSTRACT FROM AUTHOR]

We introduce and discuss a class of generalized vector complementarity problems with moving cones. We discuss the existence results for the generalized vector complementarity problem under inclusive type condition. We obtain equivalence results between the generalized vector complementarity problem, the generalized vector variational inequality problem, and other related problems. The theorems presented here improve, extend, and develop some earlier and very recent results in the literature. [ABSTRACT FROM AUTHOR]

The article discusses the finite-step relaxed hybrid steepest-descent method for variational inequalities. The finite-step relaxed hybrid steepest-descent method is used to address the classical variational inequality problem of a monotone operator on a nonempty closed convex subset in a Hilbert space. The strong convergence of the finite-step relaxed hybrid steepest-descent method involves projection to compute the complexity of the convex set and was established under proper assumptions that are imposed on the algorithm parameters.

The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters. [ABSTRACT FROM AUTHOR]

The article presents a study on the solvability for a class of generalized strong vector variational-like inequalities in reflexive Banach spaces. The use of Brouwer's fixed point theorem proved the solvability of these inequalities without monotonicity assumption under some conditions. Fan's lemma and Nadler's theorem also proved the solvability of these inequalities and introduced a new concept of pseudomonotonicity for pseudomonotone vector multifunctions. It is concluded that the study extends and improve the corresponding results of Fang and Huang study that was conducted in 2006.

The main object of this paper is to establish some fixed point theorems for a family of multivalued maps defined on the product of Hauedorff topological vector spaces. From our fixed point theorems, we derive some maximal element theorems for a family of multivalued maps. As an application of our results, we prove an equilibrium existence theorem for non-compact abstract economy. The results of this paper generalize known results in the literature. [ABSTRACT FROM AUTHOR]