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The relativistic quantum dynamics of the generalized Klein-Gordon (KG)oscillator having position-dependent mass in the G\"{o}del-type space-time isinvestigated. We have presented the generalized KG oscillator in thisspace-time, and discussed the effect of Cornell potential and linear potentialfor our considered system. The modification from the parameters ofposition-dependent mass and characterizing the space-time for the energyspectrums are presented.

The generalized Klein-Gordon oscillator with position-dependent mass in a particular G\"{o}del-type space-time