  The system of tensor equations (TEs) has received much considerable attention
in the recent literature. In this paper, we consider a class of generalized
tensor equations (GTEs). An important difference between GTEs and TEs is that
GTEs can be regarded as a system of non-homogenous polynomial equations,
whereas TEs is a homogenous one. Such a difference usually makes the
theoretical and algorithmic results tailored for TEs not necessarily applicable
to GTEs. To study properties of the solution set of GTEs, we first introduce a
new class of so-named ${\rm Z}^+$-tensor, which includes the set of all
P-tensors as its proper subset. With the help of degree theory, we prove that
the system of GTEs with a leading coefficient ${\rm Z}^+$-tensor has at least
one solution for any right-hand side vector. Moreover, we study the local error
bounds under some appropriate conditions. Finally, we employ a
Levenberg-Marquardt algorithm to find a solution to GTEs and report some
preliminary numerical results.
