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In the current note, we study Lorentzian para-Kenmotsu (in brief,$LP$-Kenmotsu) manifolds admitting Ricci-Yamabe solitons (RYS) and gradientRicci-Yamabe soliton (gradient RYS). At last by constructing a 5-dimensionalnon-trivial example we illustrate our result.

A note on $LP$-Kenmotsu manifolds admitting Ricci-Yamabe solitons