The representation and continuity of a generalized metric projection onto half-spaces in banach spaces

In this paper, we will give a distance formula under p_ C from a point to a half-space K_{ x^ ∗_ 0 , c} = { x ∈ X : x^ ∗_ 0 ( x ) ≤ c } in Banach space and investigate the continuity of this generalized metric projection, extending corresponding results for the case of norm.