Abstarct: In this thesis we study the strong conical hull intersection property completely characterizes the best approximation to x in a hilbert space X from the set K := C ∩ {x ∈ X : −g(x) ∈ S} by a perturbation x − l of x from the set C for some l in a convex cone of X. where C is a closed convex subset of X. S is closed convex cone which does not necessarily have non-empty interior. Y is a banach space and g : X → Y is a continuous S-convex function.