The essential components of the set of equilibrium points for set-valued maps

Yu, Jian; Yang, Hui

doi:10.1016/j.jmaa.2004.06.042

Cited by 10 publications

(4 citation statements)

References 8 publications

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“…Several authors (i.e. Yang and Yu, 2002;Yu and Yang, 2004;Lin, 2005) have demonstrated that the fixed point theory can be applied to optimisation problems, game theory problems, and also in problems related to the Nash equilibrium.…”

Section: Illustrating the Interconnection Between The Theoriesmentioning

confidence: 99%

About Applications of the Fixed Point Theory

Bucur

2017

Scientific Bulletin

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The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

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Section: Illustrating the Interconnection Between The Theoriesmentioning

confidence: 99%

About Applications of the Fixed Point Theory

Bucur

2017

Scientific Bulletin

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“…Because Q is a second category set, we may say that, in the sense of Baire category, the property P holds for most of the points in Y . The research on generic properties (including generic existence, generic uniqueness, generic stability and generic well‐posedness) has attracted much attention (see, for example, ). We also note that the Baire category and the category by measurements are different (see the following example). Example Let 0 < α < 1.…”

Section: Existence and Stability Analysis Of Optimal Controlmentioning

confidence: 99%

“…Yu and Carbonell‐Nicolau extended the notion and the results to general n‐person non‐cooperative games. Recently, the concept of essentiality has been widely used in studying the stability of solutions in various nonlinear problems including optimization problems, fixed point problems, Ky Fans point problems, Nash equilibrium problems, and KKM point problems (see, for instance, ).…”

Section: Introductionmentioning

confidence: 99%

Existence and stability analysis of optimal control

Liu

Peng

et al. 2013

Optim Control Appl Methods

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By constructing a complete metric space and a compact set of admissible control functions, this paper investigates the existence and stability of solutions of optimal control problems with respect to the right-hand side functions. On the basis of set-valued mapping theory, by introducing the notion of essential solutions for optimal control problems, some sufficient and necessary criteria guaranteeing the existence and stability of solutions are established. New derived criteria show that the optimal control problems whose solutions are all essential form a dense residual set, and so every optimal control problem can be closely approximated arbitrarily by an essential optimal control problem. The example shows that not all optimal control problems are stable. However, our main result shows that, in the sense of Baire category, most of the optimal control problems are stable.

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“…Essential sets of KKM points under the perturbation of KKM mappings were studied in [9], and Essential Sets of Fixed Points 943 further studies on essential components of generalized KKM points were given in [10]. Yu and Yang also proved some results on essential sets of equilibrium points under the perturbation of set-valued maps [11].…”

Section: Introductionmentioning

confidence: 99%

On Essential Sets of Fixed Points for Functions

Song

2015

Numerical Functional Analysis and Optimization

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This article studies essential stabilities of fixed points under the dual perturbations of functions and domains using uniform topology. We show that each fixed point for most functions has the ability to resist these dual perturbations. The existence result of minimal essential sets of fixed points is established, and the connectedness of minimal essential sets is proved under some conditions. These generalize some corresponding results in references.

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The essential components of the set of equilibrium points for set-valued maps

Cited by 10 publications

References 8 publications

About Applications of the Fixed Point Theory

About Applications of the Fixed Point Theory

Existence and stability analysis of optimal control

On Essential Sets of Fixed Points for Functions

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