It is well known that in compact local Lipschitz neighborhood retracts in Rn flat convergence for Euclidean integer rectifiable currents amounts just to weak convergence. The purpose of the present paper is to extend this result to integral currents in complete metric spaces admitting a local cone type inequality. This includes for example all Banach spaces and complete CAT(κ)-spaces, κ ∈ R. Th...

In this paper we obtain a unique common fixed point theorem for three pairs of weakly compatible mappings in D∗-cone metric spaces.

In this paper, some new fixed point theorems for generalized contractive type mappings in cone metric spaces are established. Mathematics Subject Classification: 47H10, 54H25

In this paper, we introduce cone metric spaces with w−distance on X. Then we prove fixed point theorems of weakly contractive, weakly Caristi. Mathematics Subject Classification: 37C25

We give a new notion of angle in general metric spaces; more precisely, given a triple a points p, x, q in a metric space (X, d), we introduce the notion of angle cone ∠pxq as being an interval ∠pxq := [∠pxq,∠ + pxq], where the quantities ∠ ± pxq are defined in terms of the distance functions from p and q via a duality construction of differentials and gradients holding for locally Lipschitz fu...

We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone R of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance matrix is defined and we proved that the set of such matrices is everywhere dense Gδ set in weak topology in the cone R. Universality of distance matrix is the necess...

We introduce the notions of the asymptotic SMK-sequence with respect to the stronger MeirKeeler cone-type mapping ξ : int P ∪ {θ} → 0, 1 and the asymptotic WMK-sequence with respect to the weaker Meir-Keeler cone-type mapping φ : int P ∪ {θ} → int P ∪ {θ} and prove some common fixed point theorems for these two asymptotic sequences in cone metric spaces with regular cone P . Our results general...

Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for s-Contraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric ...