I have problems with this demostration can anybody help me please? If $X$ is a compact space and $A:X\rightarrow X$ is such that $\rho(Ax,Ay)<\rho(x,y)$, $x\neq y, \Rightarrow A $ have only one fix point on X.
2026-04-02 11:42:19.1775130139
If $X$ is a compact space and $A:X\rightarrow X$ is such that $\rho(Ax,Ay)<\rho(x,y)$, $x\neq y, \Rightarrow A $ have only one fix point on X.
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Um, if x and y are two unequal fixed points then $\rho(Ax,Ay)= \rho(x,y)$.
So there can't be more than one fixed point.