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.

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 LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS

2009 ◽  
Vol 81 (1) ◽  
pp. 85-95 ◽  
Author(s):  
SHENG-JIE LI ◽  
HUI-MIN LIU ◽  
CHUN-RONG CHEN
Keyword(s):  
Equilibrium Problem ◽  
Lower Semicontinuity ◽  
Equilibrium Problems ◽  
Sufficient Conditions ◽  
Vector Equilibrium Problems ◽  
Solution Mapping ◽  
Scalarization Method ◽  
Set Valued Mappings ◽  
Vector Equilibrium ◽  
Weak Vector

AbstractIn this paper, using a scalarization method, we obtain sufficient conditions for the lower semicontinuity and continuity of the solution mapping to a parametric generalized weak vector equilibrium problem with set-valued mappings.

scholarly journals Hölder Continuity of a Parametric Generalized Variational Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li-na Wang ◽  
Xiao-bing Li
Keyword(s):  
Variational Inequality ◽  
Projection Method ◽  
Hölder Continuity ◽  
Sufficient Conditions ◽  
Metric Projection ◽  
Holder Continuity ◽  
Data Perturbation ◽  
Generalized Variational Inequality ◽  
Solution Mapping

By using the classic metric projection method, we obtain sufficient conditions for Hölder continuity of the nonunique solution mapping for a parametric generalized variational inequality with respect to data perturbation. The result is different from the recent ones in the literature and has a strong geometric flavor.

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