  $f(T,B)$ teleparallel gravity is a recently proposed straightforward
generalization of the popular $f(T)$ teleparallel gravity by the incorporation
of a boundary term $B=\frac{2}{e}\partial_{i}(e T ^{i}) =
\bigtriangledown_{i}T^{i}$ where $T$ denote the torsion scalar \cite{ftb13}. In
this work, I investigate the viability of some well motivated $f(T,B)$
teleparallel gravity models of the forms $f=\alpha B^n+\beta T^m$, $f=\alpha
B^n T^m$ and $f=\alpha \log (B)+\beta T$ where $\alpha, \beta, n$ and $m$ are
free parameters from the inequalities imposed the the weak energy condition. I
use the recent estimates of Hubble, deceleration, jerk and snap parameters in
finding corners in parameter spaces for the cosmological models for which the
energy density remain positive and the weak energy condition ( i.e, $\rho+p
\geq 0$, where $p$ and $\rho$ represent respectively the cosmological pressure
and energy density) attains a minute positive value, as this implies the EoS
parameter $\omega = p/\rho \simeq-1$ and therefore consistent with an
accelerating universe.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics