scholarly journals Maximal Element Theorems In GFC-Spaces With The Application To Systems of General Quasiequilibrium Problems

2016 ◽  
Author(s):  
Kaiting Wen
Keyword(s):  
Maximal Element ◽  
Quasiequilibrium Problems

The Equilibrium Existence Theorem for Systems of General Quasiequilibrium Problems in GFC-Spaces

2014 ◽  
Vol 556-562 ◽  
pp. 4128-4132
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Kkm Mapping ◽  
Kkm Theorem ◽  
Equilibrium Existence ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Matching Theorem ◽  
Element Theorem

In this paper, the GFC-KKM mapping is introduced and a GFC-KKM theorem is established in GFC-spaces. As applications, a matching theorem and a maximal element theorem are obtained. Our results unify, improve and generalize some known results in recent reference. Finally, an equilibrium existence theorem for systems of general quasiequilibrium problems is yielded in GFC-spaces.

A New Maximal Theorem in Product GFC-Spaces with Application to Systems of Generalized Mixed Vector Quasiequilibrium Problems

2013 ◽  
Vol 405-408 ◽  
pp. 3151-3154
Author(s):  
Kai Ting Wen
Keyword(s):  
Existence Theorem ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Quasi Equilibrium ◽  
Quasiequilibrium Problems ◽  
Maximal Element Theorem ◽  
Maximal Theorem ◽  
Vector Quasiequilibrium Problems ◽  
Element Theorem

In this paper, a new maximal element theorem is established in product GFC-spaces. As application, a new existence theorem of solutions for systems of generalized mixed vector quasi-equilibrium problems is obtained.

scholarly journals A maximum principle

1979 ◽  
Vol 28 (1) ◽  
pp. 23-26
Author(s):  
Kung-Fu Ng
Keyword(s):  
Maximum Principle ◽  
Extreme Point ◽  
Convex Space ◽  
Maximal Element ◽  
Locally Convex Space ◽  
Compact Set ◽  
Natural Manner ◽  
Upper Semicontinuous ◽  
Nonempty Compact ◽  
Locally Convex

AbstractLet K be a nonempty compact set in a Hausdorff locally convex space, and F a nonempty family of upper semicontinuous convex-like functions from K into [–∞, ∞). K is partially ordered by F in a natural manner. It is shown among other things that each isotone, upper semicontinuous and convex-like function g: K → [ – ∞, ∞) attains its K-maximum at some extreme point of K which is also a maximal element of K.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 46 A 40.

scholarly journals Painleve-Kuratowski convergences of the approximate solution sets for vector quasiequilibrium problems

2018 ◽  
Vol 34 (1) ◽  
pp. 115-122
Author(s):  
NGUYEN VAN HUNG ◽  
◽  
DINH HUY HOANG ◽  
VO MINH TAM ◽  
◽  
...  
Keyword(s):  
Approximate Solution ◽  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Quasiequilibrium Problems ◽  
Solution Sets ◽  
Special Cases ◽  
Vector Quasiequilibrium Problems

In this paper, we study vector quasiequilibrium problems. After that, the Painlev´e-Kuratowski upper convergence, lower convergence and convergence of the approximate solution sets for these problems are investigated by using a sequence of mappings ΓC -converging. As applications, we also consider the Painlev´e-Kuratowski upper convergence of the approximate solution sets in the special cases of variational inequality problems of the Minty type and Stampacchia type. The results presented in this paper extend and improve some main results in the literature.

scholarly journals Strong admissibility for abstract dialectical frameworks

2021 ◽  
pp. 1-41
Author(s):  
Atefeh Keshavarzi Zafarghandi ◽  
Rineke Verbrugge ◽  
Bart Verheij
Keyword(s):  
Maximal Element ◽  
Decision Problems ◽  
Current Work ◽  
Argument Evaluation ◽  
Abstract Argumentation ◽  
Proper Generalization

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: (1) whether a given interpretation is a strongly admissible interpretation of a given ADF, and (2) whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs.

Levitin-Polyak well-posedness for parametric quasivariational inclusion and disclusion problems

2018 ◽  
Vol 34 (3) ◽  
pp. 295-303
Author(s):  
PANATDA BOONMAN ◽  
◽  
RABIAN WANGKEEREE ◽  
Keyword(s):  
Equilibrium Problem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Well Posedness ◽  
Quasiequilibrium Problems ◽  
Necessary And Sufficient

In this paper, we aim to suggest the new concept of Levitin-Polyak (for short, LP) well-posedness for the parametric quasivariational inclusion and disclusion problems (for short, (QVIP) (resp. (QVDP))). Necessary and sufficient conditions for LP well-posedness of these problems are proved. As applications, we obtained immediately some results of LP well-posedness for the quasiequilibrium problems and for a scalar equilibrium problem.

Maximal element with applications to Nash equilibrium problems in Hadamard manifolds

Optimization ◽  
2019 ◽  
Vol 68 (8) ◽  
pp. 1491-1520
Author(s):  
Hai-Shu Lu ◽  
Rong Li ◽  
Zhi-Hua Wang
Keyword(s):  
Nash Equilibrium ◽  
Maximal Element ◽  
Equilibrium Problems ◽  
Hadamard Manifolds

scholarly journals Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Shu-qiang Shan ◽  
Yu Han ◽  
Nan-jing Huang
Keyword(s):  
Nash Equilibria ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Upper Semicontinuity ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Quasiequilibrium Problems ◽  
Parametric Variational Inequality ◽  
Parametric Optimization Problem ◽  
Vector Quasiequilibrium Problems

We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.

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