A topological vector space valued cone metric space is a generalization of a cone metric space in the sense that the ordered Banach space in the definition is replaced by an ordered locally convex Hausdorff topological vector space
. The author obtains a metric
on a topological vector space valued cone metric space
is a nonlinear scalarization function defined as
is the pointed convex cone. He proves an interesting theorem which is equivalent to the Banach contraction principle.