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Motivated by recent developments of black hole thermodynamics in de Rham,Gabadadze and Tolley(dRGT) massive gravity, we study the critical behaviors offour-dimensional topological Anti-de Sitter(AdS) black holes in the presence ofBorn-Infeld nonlinear electrodynamics by treating the cosmological constant aspressure and the corresponding conjugate quantity is interpreted asthermodynamic volume. It shows that besides the Van der Waals-like SBH/LBHphase transitions appears, the so-called reentrant phase transitions (RPTs) arealso observed when the coupling coefficients $c_i m^2$ of massive potential andBorn-Infeld parameter $b$ satisfy some certain conditions.

Reentrant phase transitions and triple points of topological AdS black holes in Born-Infeld-massive gravity