Caristi不动点定理的充要条件

Research on sufficiency and necessary condition of Caristi fixed point theorem

Caristi不动点定理是一个值得十分重视和非常有趣的不动点定理,这一结果已被应用于研究内向映像的理论和正规可解性理论.考虑到寻找满足:d(x,Tx)≤xφTx x∈X条件的映射φ是一件相当困难的事,本文将给出准存在且满足上述条件的一个充分必要条件,使我们的工作更具有可操作性.

Fixed point theory has received great attention at all times. This result has been applied in the research introverted reflection theory and the regular soluble theory. In this paper, we gives a sufficiency and necessary condition of existence of function d （x, Tx） ≤Фx - ФTx axbitary x ∈ X satisfying Caristi fixed point theorem.