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In this letter we choose generalized Ayon Beato Gracia (ABG) magnetic chargedblack hole with five parameters to investigate possibility of thermodynamicphase transition and coexistence of different gass/liquid/solid phases of thisblack hole. In fact this work is an extension of our recently work where ABGblack hole with three parameters was used to seek the phase transition. In thiswork we obtain other physical values on the parameters with respect to ourprevious work where the phase transition is happened together with coexistencepoint of different phases in the phase space.

Magnetic charge effects on thermodynamic phase transition of modified Anti de Sitter Ay\'{o}n-Beato-Garc\'{i}a Black Holes with five parameters