  The primary objective of this paper is to propose and analyze the notion of
dual cones associated with the metric projection and generalized projection in
Banach spaces. We show that the dual cones, related to the metric projection
and generalized metric projection, lose many important properties in
transitioning from Hilbert spaces to Banach spaces. We also propose and analyze
the notions of faces and visions in Banach spaces and relate them to the metric
projection and generalized projection. We provide many illustrative examples to
give insight into the given results.
