  We introduce tensor generalized bilateral inverses (TGBIs) under the Einstein
tensor product as an extension of generalized bilateral inverses (GBIs) in the
matrix environment. Moreover, the TBGI class includes so far considered
composite generalized inverses (CGIs) for matrices and tensors. Applications of
TBGIs for solving multilinear systems are presented. The characterizations and
representations of TGBI were studied and verified using a specific algebraic
approach. Further, a few characterizations of known CGIs (such as CMP, DMP,
MPD, MPCEP, and CEPMP) are derived. The main properties of the TGBIs ware
exploited and verified through numerical examples.
