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...

Exponential functionals of Lévy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process. Further we use these results to investigate properties of the mapping Φ, which maps two independent Lévy processes to their corresponding exponential functional...

Recently, Choudhury and Metiya [Fixed points of weak contractions in cone metric spaces, Nonlinear Analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. Weak contractions are generalizations of the Banach's contraction mapping, which have been studied by several authors. In this paper, we introduce the notion of $f$-weak contractions and als...

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...

In the present work, we have introduced a new type of (ξ,ω)-weakly cyclic generalized contraction in setting metric spaces and established some fixed-point results. Fixed-point results are useful establishing existence unique solution to differential equations. We supplemented derived with suitable non-trivial examples an application Boundary Value Problem, generalizing known The analytical res...

In this paper, we introduce cyclic weak φ−contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.