Exsting Error In Tally 9.0

A version of the fixed point theorem of Banach type integral

8.Notation be denoted by IN (f, 0, a) the integral of f over

the interval [0, a] in IR.

Let (E, d) a metric space complet.T

is an application of E into E satisfying:

exists k in (0,1 [such that:

IN (f, 0, d (Tx Ty))

where f is a function of IR ^ {+} in IR ^{+}, locally summable and for every \\ epsilon> 0,

IN (f, 0, \\ epsilon)> 0.

Prove that T admits a unique fixed point z and

any x in E the sequence {T} x ^ {n} converges to z.

Compare this result with the fixed point theorem of Banach

.

(From Branciari.Voir message references)
<=k IN(f,0,d(x,y)) , sur ExE