文献类型：会议论文

英文题名：Well Posedness of Generalized Mutually Minimization Problem

作者：Ni, Ren-Xing[1]

机构：[1]Shaoxing Univ, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China

会议论文集：2nd International Conference on Information and Computing Science

会议日期：MAY 21-22, 2009

会议地点：Manchester, ENGLAND

语种：英文

外文关键词：well posed; relatively boundedly weakly compact subset; minimization sequence; dense subset; generalized mutually minimization problem

外文摘要：Let C be a closed bounded convex subset of a Banach space X with 0 being an interior point of C and p(C)(.) be the Minkowski functional with respect to C. Let B(X) be the family of nonempty bounded closed subset of X endowed with the Hausdorff distance. A generalized mutually minimization problem min(C)(F,G) is said to be well posed if it has a unique solution (x. z) and every minimizing sequence converges strongly to (x. z). Under the assumption that C is both strictly convex and Kadec, G is a nonempty closed, relatively boundedly weakly compact subset of X, using the concept of the admissible family M of B(X), we prove the generic result that the set E of all subsets F such that the generalized mutually minimization problem min(C)(F,G) is well posed is a dense subset of M. These extend and sharpen some recent results due to De Blasi, Myjak and Papini, Li, Li and Xu, and Ni, etc.