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Two-dimensional (\$2D\$) Lifshitz-like black holes in special \$F(R)\$ gravity
cases are extracted. We indicate an essential singularity at \$r=0\$, covered
with an event horizon. Then conserved and thermodynamic quantities such as
temperature, mass, entropy, and the heat capacity of \$2D\$ Lifshitz-like black
holes in \$F(R)\$ gravity are evaluated. Our analysis shows that \$2D\$
Lifshitz-like black hole solutions can be physical solutions, provided that the
cosmological constant is negative (\$\Lambda<0\$). Indeed, there is a phase
transition between stable and unstable cases by increasing the radius of AdS
black holes. In other words, the \$2D\$ Lifshitz-like AdS black holes with large
radii are physical and enjoy thermal stability. The obtained \$2D\$ Lifshitz-like
AdS-black holes in \$F(R)\$ gravity turn to the well-known \$2D\$ Schwarzschild
AdS-black holes when the Lifshitz-like parameter is zero (\$s=0\$). Also,
correspondence between these black hole solutions and the \$2D\$ rotating black
hole solutions is found by adjusting the Lifshitz-like parameter.

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