Extended <Emphasis Type="Italic">B</Emphasis>-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity

The purpose of this paper is to study the extended well-posedness in the sense of Bednarczuk for set-valued vector optimization. This notion of well-posedness can be interpreted as some sort of well-posedness under perturbation in terms of Hausdorff set-convergence. To investigate the extended B-well-posedness, we generalize property (H) due to Miglierina and Molho to the set-valued and perturbed case. Under a convexity assumption, we show that the extended B-well-posedness is closely related to property (H). This work was supported by the Scientific Research Foundation of CUIT (CRF200704), the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005).