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In this paper, we obtained Liouville theorem for $ \phi $-$F$-symphonic map ,$ \phi $-$F$-harmonic map and $ \phi $-$\Phi_{S, p, \varepsilon}$ harmonic mapwith free boundary on metric measure space.

Liouville theorem for $ \phi $-$F$-symphonic map , $ \phi $-$F$-harmonic  map and and $ \phi $-$\Phi_{S, p, \varepsilon}$ harmonic map with free  boundary