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We intend to study a new class of cosmological models in $f(R, T)$ modifiedtheories of gravity, hence define the cosmological constant $\Lambda$ as afunction of the trace of the stress energy-momentum-tensor $T$ and the Ricciscalar $R$, and name such a model "$\Lambda(R, T)$ gravity" where we havespecified a certain form of $\Lambda(R, T)$. $\Lambda(R, T)$ is also defined inthe perfect fluid and dust case. Some physical and geometric properties of themodel are also discussed. The pressure, density and energy conditions arestudied both when $\Lambda$ is a positive constant and when$\Lambda=\Lambda(t)$, i.e a function of cosmological time, t. We study thebehaviour of some cosmological quantities such as Hubble and decelerationparameters. The model is innovative in the sense that it has been described interms of both $R$ and $T$ and display a better understanding of thecosmological observations.

(2+1) dimensional cosmological models in f(R; T) gravity with $\Lambda$(R; T)