We have $f,g:R\rightarrow R$ two contractions with the same fixed point and $(x_{n})_{n\geq1}$ a sequence with real numbers with the propriety that $x_{n+1}\in \left\{f(x_{n}),g(x_{n})\right\}$, for any $n\geq1$. Show that $(x_{n})_{n\geq1}$ is convergent.
2026-02-27 14:45:07.1772203507
Two contractions with the same fixed point. Show that this sequence is convergent
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