  Traversable wormholes, tunnel like structures introduced by Morris \& Thorne
\cite{morris1}, have a significant role in connection of two different
space-times or two different parts of the same space-time. The characteristics
of these wormholes depend upon the redshift and shape functions which are
defined in terms of radial coordinate. In literature, several shape functions
are defined and wormholes are studied in $f(R)$ gravity with respect to these
shape functions \cite{lobo, saiedi, baha}. In this paper, two shape functions
(i) $b(r)=\dfrac{{r_0} \log (r+1)}{\log ({r_0}+1)}$ and (ii)
$b(r)=r_0(\frac{r}{r_0})^\gamma$, $0<\gamma<1$ are considered. The first shape
function is newly defined, however the second one is collected from the
literature\cite{cataldo}. The wormholes are investigated for each type of shape
function in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $m$,
$n$, $\alpha$, and $\beta$ are real constants. Varying parameters $\alpha$ or
$\beta$, $f(R)$ model is studied in five subcases for each type of shape
function. In each case, the energy density, radial \& tangential pressures,
energy conditions that include null energy condition, weak energy condition,
strong energy condition \& dominated energy condition, and anisotropic
parameter are computed. The energy density is found to be positive and all
energy conditions are obtained to be violated which supports the existence of
wormholes. Also, the equation of state parameter is obtained to possess values
less than -1, that shows the presence of the phantom fluid and leads towards
the expansion of the universe.
