Generalized KKM theorems and common fixed point theorems

The purpose of this article is to establish some results on the existence and generic stability of solution sets of the controlled system for multiobjective generalized games in infinite-dimensional spaces. First, we introduce a class of the controlled system for multiobjective generalized games. Afterward, we establish some conditions for existence of the solution set to this problem using the Kakutani-Fan-Glicksberg fixedpoint theorem. Finally, we study the generic stability of set-valued mappings where the set of essential points of a map is a dense residual subset of a (Hausdorff) metric space of the set-valued maps. The results presented in the paper are new and completely different from the main results given by some authors in the literature.

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“…Then, there exists x 0 ∈ N such that N (x 0 ) = ∅. Lemma 2.4 (Kakutani-Fan-Glicksberg fixed-point theorem, see [5,12])…”

Section: Introductionmentioning

confidence: 99%

Existence and generic stability conditions of equilibrium points to controlled systems for n-player multiobjective generalized games using the Kakutani–Fan–Glicksberg fixed-point theorem

Hùng

Keller

2021

Optim Lett

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“…In this pape, inspired by the works [1,4,5,9,11,14,17,18,21,22,23,24,25], we give some existence results for the solutions of the problems (2)-(4) and also discuss the coincidence point results.…”

Section: Introductionmentioning

confidence: 99%

General set-valued vector variational inequality problems

2017

Commun. Optim. Theory

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“…Recently, many scholars (see [18][19][20][21]) not only studied further the theorem involving mapping, but also established some new theorem, fixed-point theorems, and coincidence theorems and utilized them to research the existence of solution to generalized vector equilibria, which makes the theory more perfect and rich. In this paper, we first introduce the new generalized class ( , , ) consisting of all multifunctions : → 2 2 Abstract and Applied Analysis that have the generalized property and prove some theorems for Amapping.…”

Section: Introductionmentioning

confidence: 99%