Connectedness of solution sets of vector equilibrium problems
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Abstract
This paper investigates a vector equilibrium problem in a topological vector space. By employing a scalarization approach together with suitable assumptions, sufficient conditions for the connectedness of the solution set of the considered problem are established. The obtained results are new in comparison with existing results in the literature and make a significant contribution to the study of solution properties in equilibrium problem theory.
Tóm tắt
Bài báo được thực hiện nhằm nghiên cứu bài toán cân bằng véc-tơ trong không gian tô pô tuyến tính. Bằng cách sử dụng phương pháp vô hướng hóa kết hợp với các giả thiết thích hợp, các điều kiện đủ cho tính liên thông của tập nghiệm bài toán đang xét được thiết lập. Kết quả đạt được là mới hơn so với các kết quả đã được công bố trước đây và là những đóng góp có ý nghĩa cho chủ đề nghiên cứu tính chất nghiệm trong lý thuyết bài toán cân bằng.
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