Kannan压缩映像的逆问题

称空间(X,d)上的自映像f为Kannan压缩映像,若对于,成立d(f(x),f(y))≤a{d(x,f(x))+d(y,f(y)}, 其中0<α<1/2。 Kannan压缩映像是Banach压缩映像的重要推广,特别在Banach压缩映像已被许多作者推广为形式多样的情况下(例如见8],那里归纳出250个压缩映像定义),重要性尤其突出。本文通过对Kannan压缩映像逆问题的证明,把相当一部分形式不同的压缩映像统一归并为Kannan压缩映像。

A Converse to Kannan's Contractive Mapping

Mang authors have generalized the well-known Banach contraction principle, among these, Kannan's contractive mapping is very important. In this paper, we establish a theorem about converse to Kannan's contractive mapping. The converse problem is not only interesting in mathemetics itself, but also useful. By this, we can see that a lot of contractive type mappings are equivalence to Kannan's contractive mapping.