and Applied Analysis 3 for all x, y ∈ E. The least positive number K satisfying the above condition is called the normal constant of P . It is clear that K ≥ 1. Definition 2.1 see 9 . Let X be a nonempty set and E a real Banach space equipped with the partial ordering with respect to the cone P . Suppose that the mapping d : X × X → E satisfies the following conditions: 1 θ d x, y for all x, y ...

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 ...

In this paper, we establish some new coupled fixed point theorems in complete metric spaces, using a new concept of F -invariant set. We introduce the notion of fixed point of N -order as natural extension of that of coupled fixed point. As applications, we discuss and adapt the presented results to the setting of partially ordered cone metric spaces. The presented results extend and complement...

We study metric properties of the cone of homogeneous non-negative multivariate polynomials and the cone of sums of powers of linear forms, and the relationship between the two cones. We compute the maximum volume ellipsoid of the natural base of the cone of nonnegative polynomials and the minimum volume ellipsoid of the natural base of the cone of powers of linear forms and compute the coeffic...