Article

Sensitivity analysis for a system of parametric generalized mixed quasi-variational inclusions involving (K,η)-monotone mappings

College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, PR China
Applied Mathematics and Computation 01/2009; DOI:10.1016/j.amc.2009.03.070 pp.318-327
Source: DBLP

ABSTRACT In this paper, we introduce a new system of parametric generalized mixed quasi-variational inclusions involving (K,η)-monotone mappings. By using resolvent operator technique of (K,η)-monotone mappings and the property of fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set for the system of parametric generalized mixed quasi-variational inclusions in Hilbert spaces. In particular, we prove that the solution set of the system of parametric generalized mixed quasi-variational inclusions is nonempty closed, and the Lipschitz continuity of solution set with respect to the parameters is also proved under suitable conditions. These results improve, unify and generalize many corresponding known results in literature.

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Keywords

Hilbert spaces
 
Lipschitz continuity
 
new system
 
parametric generalized mixed quasi-variational inclusions
 
resolvent operator technique
 
set-valued contractive mappings
 
suitable conditions
 

Xie Ping Ding