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In this paper, we construct a new class of solutions for five dimensional third order quasitopological black holes coupled to a power-law Maxwell nonlinear electrodynamics. To have real solutions, we should establish condition µ < − λ 2 3 and to have finite solutions at infinity, the parameter of power-law Maxwell theory "s" should obey 1 2 < s ≤ 2. Power-law Maxwell lagrangian is successful to set conformal invariance in higher dimensions. Also, this theory can reduce the divergence of the electrical field at the origin that is caused in linear Maxwell theory. As the value of parameter "s" increases, this divergence reduces more. In asymptotically anti-de sitter spacetimes, these obtained solutions lead to a black hole with two horizons for small values of s and q. Also, solutions for s = 2 have different behaviors with respect to the ones for other values of s. For negative and small values of parameter µ, these solutions can describe a black hole with two horizons. An other important tip is that this black hole has thermal stability just for anti-de sitter solutions if its temperature is positive.

It was shown that with the combination of three Liouville-type dilaton potentials, one can derive dilaton black holes in the background of anti-de-Sitter (AdS) spaces. In this paper, we further extend the study on the dilaton AdS black holes by investigating their thermodynamic instability through a geometry approach. First, we review thermodynamic quantities of the solutions and check the validity of the first law of thermodynamics. Then, we investigate phase transitions and stability of the solutions. In particular, we disclose the effects of the dilaton field on the stability of the black holes. We also employ the geometrical approach toward thermodynamical behavior of the system and find that the divergencies in the Ricci scalar coincide with roots and divergencies in the heat capacity. We find that the behavior of the Ricci scalar around divergence points depends on the type of the phase transition.

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