  Formation of specific static wormhole models is discussed, by assuming an
$f(\textit{R}, \textit{T}) = R + 2 \lambda T$ extended theory of gravity, $T =-
\rho + P_{r} + 2P_{l}$ being the trace of the energy momentum tensor. In the
first part, wormhole solutions are constructed imposing that the radial
pressure admits an equation of state corresponding to a varying Chaplygin gas.
Two forms for the varying Chaplygin gas are considered, namely $P_{r} = - B
b(r)^{u}/\rho^{\alpha}$ and $P_{r} = -B R(r)^{m}/ \rho^{\alpha }$,
respectively. In the second part, the wormhole models are constructed assuming
that the radial pressure can be described by a varying barotropic fluid. In
particular, $P_{r} = \omega b(r)^{v} \rho$ and $P_{r} =\hat{ \omega} r^{k}
R(r)^{\eta} \rho$ are considered, respectively, leading to two additional,
traversable wormhole models. In all cases, $b(r)$ is the shape function, and
$R(r)$ the Ricci scalar obtained from the wormhole metric for a redshift
function equal to $1$. With the help of specific examples, it is demonstrated
that the shape functions of the exact wormhole models previously constructed do
obey the necessary metric conditions. The same energy conditions help reveal
the physical properties of these models. A general feature is the violation of
the NEC~($\rho + P_{i} \geq 0$) in terms of the radial pressure $P_{r}$ at the
throat of the wormhole. For some of the models, one can satisfy the NEC at the
throat while a violation of the DEC~($\rho - P_{i} \geq 0$) occurs. To
summarize, exact wormhole models can be constructed with a possible violation
of the NEC and DEC at the throat of the wormhole, while being $\rho \geq 0 $.
Thus, the interesting feature appears that one has a violation of the
WEC~($\rho \geq 0$ and $\rho + P_{i} \geq 0$) not related to the energy density
behavior (the index i, being r resp. l, indicates radial resp. lateral
pressure).
