Coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities

Balaj, Mircea

doi:10.1016/j.na.2007.04.033

Cited by 18 publications

(13 citation statements)

References 15 publications

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“…The results presented in this paper improve and generalize some corresponding results due to Balaj [1], Balaj and Lin [3] and Lin, Ansari and Wu [14].…”

Section: Introductionsupporting

confidence: 89%

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Coincidence Theorems for Noncompact ℜℭ-Maps in Abstract Convex Spaces With Applications

Yang¹,

Huang²

2012

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, a coincidence theorem for a compact RC-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact RC-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As applications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

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“…The results presented in this paper improve and generalize some corresponding results due to Balaj [1], Balaj and Lin [3] and Lin, Ansari and Wu [14].…”

Section: Introductionsupporting

confidence: 89%

“…On the other hand, since Fan [7] and Liu [15] extended the von NeumannSion principle obtaining two-function minimax inequalities, many such results involving two or more functions have been obtained in the literature (see, for example, [1,3,18] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Coincidence Theorems for Noncompact ℜℭ-Maps in Abstract Convex Spaces With Applications

Yang¹,

Huang²

2012

Bulletin of the Korean Mathematical Society

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“…These problems contains vector optimization, vector variational inequality problem and vector Nash equilibrium problem as special cases, see for example [2,3] and references therein.…”

Section: X mentioning

confidence: 99%

Existence of Solutions to Generalized Vector Quasi-equilibrium Problems with Set-Valued Mappings

Zhao¹,

Lu²,

Wang³

2016

Proceedings of the 2016 International Conference on Artificial Intelligence: Technologies and Applications

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Abstract-In this paper, we introduce and study a class of generalized vector quasi-equilibrium problems, which includes generalized vector quasi-variational-like inequality problems, generalized vector equilibrium problems, generalized vector variational inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of solutions for the class of generalized vector quasi-equilibrium problems without any monotonicity conditions in the setting of locally convex topological vector space. The results presented here improve and extend the corresponding results in this area.

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“…These problems, or more general equilibrium problems, are studied in many papers (see, for instance, [5,7,8,[12][13][14][15][16][17])…”

Section: Applicationsmentioning

confidence: 99%

A common fixed point theorem with applications to vector equilibrium problems

Balaj

2010

Applied Mathematics Letters

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Coincidence and maximal element theorems and their applications to generalized equilibrium problems and minimax inequalities

Cited by 18 publications

References 15 publications

Coincidence Theorems for Noncompact ℜℭ-Maps in Abstract Convex Spaces With Applications

Coincidence Theorems for Noncompact ℜℭ-Maps in Abstract Convex Spaces With Applications

Existence of Solutions to Generalized Vector Quasi-equilibrium Problems with Set-Valued Mappings

A common fixed point theorem with applications to vector equilibrium problems

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