On Multivalued Contractions in Cone Metric Spaces without Normality

Wardowski (2011) in this paper for a normal cone metric space (X, d) and for the family 𝒜 of subsets of X established a new cone metric H : 𝒜 × 𝒜 → E and obtained fixed point of set-valued contraction of Nadler type. Further, it is noticed in the work of Janković et al., 2011 that the fixed-point problem in the setting of cone metric spaces is appropriate only in the case when the underlying cone is nonnormal. In the present paper we improve Wardowski's result by proving the same without the assumption of normality on cones.