Tomas Dominguez教授讲座公告
时间:2019-07-03 17:03, 来源:数学科学学院

报告题目: Fixed point for nonexpansive mappings: an interdisciplinary area

报告人:Tomas Dominguez

时间:7月5日 9:00--10:00

地点: A10-301

摘要:Let $X$ be a metric space. A mapping $T:X\to X$ is said to be nonexpansive if $d(Tx,Ty)\leq d(x,y)$. Fixed Point Theory for nonexpansive mappings have been widely developed in the last 50 years. The existence of fixed points for nonexpansive mappings defined on a convex closed bounded subset  of a Banach space deeply depends on the geometry of the space. This fact has originated a strong connections between usual notions of Linear Functional Analysis as uniform convexity, normal structure or reflexivity and some other notions corresponding to Nonlinear Analysis as the existence of fixed points for nonlinear mappings.     In this talk we will focus on the relationship between the existence of fixed points for nonexpansive mappings under renorming   and the reflexivity. In particular, we will show the solution of a long standing problem: Every reflexive Banach space can be renormed such that every nonexpansive mapping for the new norm, defined from a convex bounded closed set $C$ into itself, has a fixed point.

研究生与学科建设处  数学科学学院

2019年7月2日

责任编辑:刘艳丽

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