Generalized Robertson–Walker Space-Times Admitting $$\boldsymbol{\eta}$$-Ricci–Yamabe Solitons

We study $$\eta$$ -Ricci–Yamabe solitons and gradient $$\eta$$ -Ricci–Yamabe solitons in generalized Robertson–Walker space-times . At first, we provide an example of an $$\eta$$ -Ricci–Yamabe soliton. Next, we prove that if a generalized Robertson–Walker space-time admits an $$\eta$$ -Ricci–Yamabe soliton or a gradient $$\eta$$ -Ricci–Yamabe soliton, then it becomes a perfect fluid space-time. As a consequence, we obtain several interesting corollaries.