B. E. Rhoades

Fixed and periodic point results in cone metric spaces

Abstract Huang and Zhang [L.-G. Haung, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] proved some fixed point theorems in cone metric spaces. In this work we prove some fixed point theorems in cone metric spaces, including results which generalize those from Haung and Zhang’s work. Given the fact that, in a cone, one has only a partial ordering, it is doubtful that their Theorem 2.1 can be further generalized. We also show that these maps have no nontrivial periodic points.

Almost convergence of double sequences and strong regularity of summability matrices

A double sequence x = { x jk : j, k = 0, 1, …} of real numbers is called almost convergent to a limit s if that is, the average value of { x jk } taken over any rectangle {( j, k ): m ≤ j ≤ m + p − 1, n ≤ k ≤ n + q − 1} tends to s as both p and q tend to ∞, and this convergence is uniform in m and n . The notion of almost convergence for single sequences was introduced by Lorentz [ 1 ].

Fixed point theorems in generalized partially ordered G-metric spaces

In this paper, we consider the concept of a @W-distance on a complete partially ordered G-metric space and prove some fixed point theorems.

Common fixed point results for noncommuting mappings without continuity in generalized metric spaces

Using the setting of a generalized metric space, a fixed point theorem is proved for one map, and several fixed point theorems are proved for two maps. These results generalize several well known comparable results in the literature.

Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type

In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature.2000 MSC: 54H25; 47H10; 54E50.

Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type

We prove a fixed point theorem for weakly compatible maps satisfying a general contractive condition of integral type.

Assad-Kirk-Type Fixed Point Theorems for a Pair of Nonself Mappings on Cone Metric Spaces

New fixed point results for a pair of non-self mappings defined on a closed subset of a metrically convex cone metric space (which is not necessarily normal) are obtained. By adapting Assad-Kirks method the existence of a unique common fixed point for a pair of non-self mappings is proved, using only the assumption that the cone interior is nonempty. Examples show that the obtained results are proper extensions of the existing ones.

Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type

AbstractWe obtain several fixed point theorems for hybrid pairs of single-valued and multivalued occasionally weakly compatible maps defined on a symmetric space satisfying a contractive condition of integral type. The results of this paper essentially contain every theorem on hybrid and multivalued self-maps of a metric space as a special case. Erratumhttp://dx.doi.org/10.1155/2008/274793

Common fixed points for four maps in cone metric spaces

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.

Property in -Metric Spaces

We prove two general fixed theorems for maps in -metric spaces and then show that these maps satisfy property .