Let $f,g:X\longrightarrow X$ be two continuous maps. Recall that $f$ and $g$ are homotopic if there exists a continuous map $F:X\times I\longrightarrow X$ so that $F(x,0)=f(x)$ and $F(x,1)=g(x)$.
Is there a known result (in connection to homotopy or homology groups) from which we can obtain $f\simeq g$?