*Correspondence: [email protected] Faculty of Mathematics and Informatics, Plovdiv University, Plovdiv, 4000, Bulgaria Abstract In this paper, we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory, we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a sol...

Since Huang and Zhang [1] introduced the concept of cone metric space, the study of common fixed points of mappings satisfying certain contractive conditions on cone metric spaces has been at the center of strong research activity, because it has not only important theoretical meaning but also wide applications. Recently, some authors obtained a number of meaningful consulting fixed point theor...

Recommended by Lech G ´ orniewicz We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

and Applied Analysis 3 effectively larger than that of the ordinary conemetric spaces. That is, every cone metric space is a cone b-metric space, but the converse need not be true. The following examples show the above remarks. Example 7. Let X = {−1, 0, 1}, E = R, andP = {(x, y) : x ≥ 0, y ≥ 0}. Define d : X × X → P by d(x, y) = d(y, x) for all x, y ∈ X, d(x, x) = θ, x ∈ X, and d(−1, 0) = (3, ...

The notion of triple fixed point was introduced by V.Berinde and M.Borcut [8] and obtained some fixed point theorems in partially ordeded metric spaces. In this paper, we obtain a unique common triple fixed point theorem in partially ordered cone metric spaces in which cone is not necessarilly normal and also mention one supported example.

In this paper we obtain some sufficient conditions for the existence of common fixed points of multivalued mappings satisfying generalized contractive conditions in non normal cone metric spaces. These results establish some of the most general common fixed point theorems for two multivalued maps in cone metric spaces. AMS subject classifications: 47H10, 54H25, 54C60, 46B40

A convex cone metric space is a cone metric space with a convex structure. In this paper, we extend an Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings to convex cone metric spaces. Our result generalizes Theorem 2 in [1].