We present some problems related to right(or bi-)invariant metrics d on the symmetric group of permutations S,. Characterizations and constructions of bi-invariant extremal (in the corresponding convex cone) metrics are given, esp. for n 6 5 . We also consider special subspaces of the metric space (S,,, d ) : unit balls, sets with prescribed distances (L-cliques), "hamiltonian" sets. Here we gi...

In 2011, Gabeleh and Akhar [3] introduced semi-cyclic-contraction and considered the existence and convergence results of best proximity points in Banach spaces. In this paper, the author introduces a cone semicyclic φ-contraction pair in cone metric spaces and considers best proximity points for the pair in cone metric spaces. His results generalize the corresponding results in [1–5]..

Recently, Azam, Arshad and Beg introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we extend the Kannan’s fixed point theorem in such spaces.

In this paper, we give the idea of a generalized c-distance in a cone b-metric space. Then, we prove some common fixed point and fixed point theorems in cone b-metric spaces by using the distance.

We provide a natural topology for a cone metric space and a noncompactness measure is defined for this space, which enables us to extend existing results for mappings and set-valued mappings defined on classical metric spaces. Moreover it is proved that the topology of any uniform topological space is generated by a cone metric. c ©2016 All rights reserved.

The solitaire cone SB is the cone of all feasible fractional Solitaire Peg games. Valid inequalities over this cone, known as pagoda functions, were used to show the infeasibility of various peg games. The link with the well studied dual metric cone and the similarities between their combinatorial structures see (3) leads to the study of a dual cut cone analogue; that is, the cone generated by ...

and Applied Analysis 3 Let X, d be an abstract metric space. The following properties are often used, particularly in the case when the underlying cone is nonnormal. The only assumption is that the cone K is solid. For details about these properties see, for example, 11 . p1 If a ha where a ∈ K and h ∈ 0, 1 , then a θ. p2 If θ u c for each c, θ c, then u θ. p3 If u v and v w, then u w. p4 If c ...