The Set-Valued Dynamic System and Its Applications to Pareto Optima |
| |
Authors: | E Tarafdar Xian-Zhi Yuan |
| |
Institution: | (1) Department of Mathematics, The University of Queensland, Brisbane, 4072 QLD, Australia 4072 |
| |
Abstract: | In this paper, we first study the existence of endpoints for set-valued dynamic systems which are either upper or lower semicontinuous in metric spaces. Then the existence, uniqueness and algorithms of endpoints for set-valued dynamic systems which are either generalized contractions (defined in metric spaces) or topological contractions (defined in topological spaces which do not necessarily have any metric). These results are then applied to derive the existence of Pareto optima for mappings which take values in ordered Banach spaces. Finally, the stability of (generalized) nucleolus sets is also established. |
| |
Keywords: | set-valued dynamic system topological contraction mapping endpoint Pareto optima Fan– Browder fixed point generalized nucleolus set stable set and maximal element |
本文献已被 SpringerLink 等数据库收录! |
|