scholarly journals A Note on Hölder Continuity of Solution Set for Parametric Vector Quasiequilibrium Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Xian-Fu Hu
Keyword(s):  
Metric Spaces ◽  
Equilibrium Problems ◽  
Hölder Continuity ◽  
Vector Equilibrium Problems ◽  
Holder Continuity ◽  
Quasiequilibrium Problems ◽  
Solution Sets ◽  
Parametric Vector Quasiequilibrium Problems ◽  
Vector Equilibrium ◽  
Vector Quasiequilibrium Problems

By using a scalarization technique, we extend and sharpen the results in S. Li and X. Li (2011) on the Hölder continuity of the solution sets of parametric vector equilibrium problems to the case of parametric vector quasiequilibrium problems in metric spaces. Furthermore, we also give an example to illustrate that our main results are applicable.

scholarly journals On System of Generalized Vector Quasiequilibrium Problems with Applications

2009 ◽  
Vol 2009 ◽  
pp. 1-10
Author(s):  
Jian-Wen Peng ◽  
Lun Wan
Keyword(s):  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Quasi Equilibrium ◽  
Vector Equilibrium Problems ◽  
Quasiequilibrium Problems ◽  
Special Cases ◽  
Vector Equilibrium ◽  
Vector Quasiequilibrium Problems ◽  
Vector Valued Functions ◽  
Vector Valued

We introduce a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases. We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of generalized quasi-equilibrium problems and the generalized Debreu-type equilibrium problem for both vector-valued functions and scalar-valued functions.

scholarly journals Hölder Continuity of Solutions to Parametric Generalized Vector Quasiequilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Y. Peng
Keyword(s):  
Recent Literature ◽  
Hölder Continuity ◽  
Sufficient Conditions ◽  
Holder Continuity ◽  
Quasiequilibrium Problems ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Quasiequilibrium Problems ◽  
Quasiequilibrium Problem ◽  
Vector Quasiequilibrium Problem

By using a linear scalarization method, we establish sufficient conditions for the Hölder continuity of the solution mappings to a parametric generalized vector quasiequilibrium problem with set-valued mappings. These results extend the recent ones in the recent literature, (e.g., Li et al. (2009), Li et al. (2011)). Furthermore, two examples are given to illustrate the obtained result.

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