  We discuss the validity of the energy conditions in a newly modified theory
named as $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity, where $R$ and $T$ represent the
scalar curvature and trace of the energy-momentum tensor. The corresponding
energy conditions are derived which appear to be more general and can reduce to
the familiar forms of these conditions in general relativity, $f(R)$ and
$f(R,T)$ theories. The general inequalities are presented in terms of recent
values of Hubble, deceleration, jerk and snap parameters. In particular, we use
two specific models recently developed in literature to study concrete
application of these conditions as well as Dolgov-Kawasaki instability.
Finally, we explore $f(R,T)$ gravity as a specific case to this modified theory
for exponential and power law models.
