SHAO Chongyang, PENG Zaiyun, LIU Fuping, WANG Jingjing. Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings[J]. Applied Mathematics and Mechanics, 2020, 41(8): 912-920. doi: 10.21656/1000-0887.400307
Citation: SHAO Chongyang, PENG Zaiyun, LIU Fuping, WANG Jingjing. Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings[J]. Applied Mathematics and Mechanics, 2020, 41(8): 912-920. doi: 10.21656/1000-0887.400307

Berge Lower Semi-Continuity of Parametric Generalized Vector Quasi-Equilibrium Problems Under Improvement Set Mappings

doi: 10.21656/1000-0887.400307
Funds:  The National Natural Science Foundation of China(11301571)
  • Received Date: 2019-10-14
  • Rev Recd Date: 2019-12-17
  • Publish Date: 2020-08-01
  • The Berge lower semi-continuity of solution mapping for a new class of parametric generalized vector quasi-equilibrium problems was discussed. Firstly, the improvement set mapping was defined, based on which the order structure was generalized and applied to the study of vector quasi-equilibrium problems, to lead to parametric generalized vector quasi-equilibrium problems under improvement set mappings (IPGVQEP). Then, a nonlinear scalarization function Ψ associated with the improvement set mapping was introduced, the scalar problem (IPGVQEP)Ψ corresponding to the above problem (IPGVQEP) was given, and the relation between solution sets of (IPGVQEP) and (IPGVQEP)Ψ was obtained. Finally, by virtue of a key hypothesis HΨ and the relation between solution sets, the sufficient and necessary conditions for Berge lower semi-continuity of the solution mapping for (IPGVQEP) were established, and an example was given to verify the results.
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