MHB Contractive Mappings: Unique Fixed Point & Notation Questions

[ozkan12]

İn compact metric space, we know that contractive mappings have a unique fixed point...And some book I see that $card{F}_{T}\le 1$...Why we use this notation ? İn my opinion we must use $card{F}_{T}=1$ ? Have you any suggestions ? Can you help me ?

 

[Ackbach]

Couple comments:

1. Try using the

\text{}

wrapper around things that want to look like regular text. So, for example, you'd type

\text{card} \, F_T \le 1

to obtain $\text{card} \, F_T \le 1$.

2. Second of all, could you please define this notation for us? I've never seen it before. Is it some sort of cardinality? And what is $F_T$? An operator? A contractive mapping?