On T-Stability of Picard Iteration in Cone Metric Spaces

i P is closed, nonempty, and P / {0}, ii a, b ∈ R, a, b ≥ 0, and x, y ∈ P imply that ax by ∈ P, iii x ∈ P and −x ∈ P imply that x 0. The space E can be partially ordered by the cone P ⊂ E; by defining, x ≤ y if and only if y − x ∈ P . Also, we write x y if y − x ∈ int P , where int P denotes the interior of P . A cone P is called normal if there exists a constant K > 0 such that 0 ≤ x ≤ y implies ‖x‖ ≤ K‖y‖. In the following we always suppose that E is a real Banach space, P is a cone in E, and ≤ is the partial ordering with respect to P .