  In general Banach spaces, the metric projection map lacks the powerful
properties it enjoys in Hilbert spaces. There are a few generalized projections
that have been proposed in order to resolve many of the deficiencies of the
metric projection. However, such notions are predominantly studied in Banach
spaces with rich topological structures, such as uniformly convex Banach
spaces. In this paper, we investigate two notions of generalized projection in
general Banach spaces. Various examples are provided to demonstrate the
proposed notions and the loss of structure in the generalized projections after
migrating from specially structured Banach spaces to general Banach spaces.
Connections between the generalized projection and the metric projection are
thoroughly explored.
