Copyright q 2011 ChiMing Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We obtain some new fixed point theorems for a ψ, φ-pair Meir-Keeler-type set-valued contraction map in metric spaces. Our main results generalize and i...

In a recent paper, Backelin, West and Xin describe a map φ∗ that recursively replaces all occurrences of the pattern k . . . 21 in a permutation σ by occurrences of the pattern (k − 1) . . . 21k. The resulting permutation φ∗(σ ) contains no decreasing subsequence of length k. We prove that, rather unexpectedly, the map φ∗ commutes with taking the inverse of a permutation. In the BWX paper, the ...

In this paper, we first introduce the new notion of rational cyclic contraction and then establish some convergence theorems of best proximity points for two non-self mappings in the frame work of complete metric space. Our results generalized and improve some main results in the literature. An example is given to support our main results.

The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $n which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function. In the following we show some results appeared in [2]. Definition 2.1 Let n1, . . . , np be posi...

Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is ...

A skew morphism of a finite group B is permutation φ that preserves the identity element and has property for every ∈ there exists positive integer ia such φ(ab) = φ(a)φia(b) all b B. The problem classifying morphisms cyclic groups notoriously hard, with no classification available up to date. Each Zn closely related specific Z|⟨φ⟩|, called quotient φ. In this paper, we use relationship other o...

Following up a recent proposal [1] for a cyclic model based on phantom dark energy, we examine the content of the contracting universe (cu) and its entropy Scu. We find that beyond dark energy the universe contains on average zero or at most a single photon which if present immediately after turnaround has infinitesimally energy which subsequently blue shifts to produce e+e− pairs. These statem...