  We consider a massless minimally coupled self interacting quantum scalar
field coupled to fermion via the Yukawa interaction, in the inflationary de
Sitter background. The fermion is also taken to be massless and the scalar
potential is taken to be a hybrid, $V(\phi)= \lambda \phi^4/4!+ \beta
\phi^3/3!$ ($\lambda >0$). The chief physical motivation behind this choice of
$V(\phi)$ corresponds to, apart from its boundedness from below property, the
fact that shape wise $V(\phi)$ has qualitative similarity with standard
inflationary classical slow roll potentials. Also, its vacuum expectation value
can be negative, suggesting some screening of the inflationary cosmological
constant. We choose that $\langle \phi \rangle\sim 0$ at early times with
respect to the Bunch-Davies vacuum, so that perturbation theory is valid
initially. We consider the equations satisfied by $\langle \phi (t) \rangle$
and $\langle \phi^2(t) \rangle$, constructed from the coarse grained equation
of motion for the slowly rolling $\phi$. We then compute the vacuum diagrammes
of various relevant operators using the in-in formalism up to three loop, in
terms of the leading powers of the secular logarithms. For a closed fermion
loop, we have restricted ourselves here to only the local contribution. These
large temporal logarithms are then resummed by constructing suitable
non-perturbative equations to compute $\langle \phi \rangle$ and $\langle
\phi^2 \rangle$. $\langle \phi \rangle$ turns out to be at least approximately
an order of magnitude less compared to the minimum of the classical potential,
$-3\beta/\lambda$, owing to the strong quantum fluctuations. For $\langle
\phi^2 \rangle$, we have computed the dynamically generated scalar mass at late
times, by taking the appropriate purely local contributions. Variations of
these quantities with respect to different couplings have also been presented.
