Abstract
In this paper, we introduce the concept of approximate Benson properly efficient solutions for the set-valued equilibrium problems (in short, SVEP) and investigate its properties. Under some suitable assumptions, the linear scalarization theorems for SVEP are obtained. Two nonlinear scalarization theorems for SVEP are presented. Based on the linear scalarization results, the nonemptiness and connectedness of the approximate Benson properly efficient solution set are established under some suitable conditions in real locally convex spaces. Some examples are also given to illustrate our results. The main results of this paper improve and generalize some known results in the literature.
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This work was supported by the National Nature Science Foundation of China (12171061) and Chongqing Talent Plan Project (cstc2024ycjh-bgzxm0081).
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Zhou, Z., Huang, F. & Ansari, Q.H. Approximate Benson properly efficient solutions for set-valued equilibrium problems. Positivity 28, 38 (2024). https://doi.org/10.1007/s11117-024-01054-3
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DOI: https://doi.org/10.1007/s11117-024-01054-3
Keywords
- Set-valued equilibrium problem
- Approximate Benson properly efficient solution
- Scalarization
- Nonemptiness
- Connectedness