  We intend to study a new class of cosmological models in $f(R, T)$ modified
theories of gravity, hence define the cosmological constant $\Lambda$ as a
function of the trace of the stress energy-momentum-tensor $T$ and the Ricci
scalar $R$, and name such a model "$\Lambda(R, T)$ gravity" where we have
specified a certain form of $\Lambda(R, T)$. $\Lambda(R, T)$ is also defined in
the perfect fluid and dust case. Some physical and geometric properties of the
model are also discussed. The pressure, density and energy conditions are
studied both when $\Lambda$ is a positive constant and when
$\Lambda=\Lambda(t)$, i.e a function of cosmological time, t. We study the
behaviour of some cosmological quantities such as Hubble and deceleration
parameters. The model is innovative in the sense that it has been described in
terms of both $R$ and $T$ and display a better understanding of the
cosmological observations.
