We show that for almost all points on any analytic curve on R which is not contained in a proper affine subspace, the Dirichlet’s theorem on simultaneous approximation, as well as its dual result for simultaneous approximation of linear forms, cannot be improved. The result is obtained by proving asymptotic equidistribution of evolution of a curve on a strongly unstable leaf under certain parti...

Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...

In this paper, we give some new coupled common  fixed point theorems for probabilistic $varphi$-contractions  in Menger probabilistic metric spaces.  As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...

Extending earlier results for analytic curve segments, in this article we describe the asymptotic behavior of evolution of a finite segment of a C-smooth curve under the geodesic flow on the unit tangent bundle of a hyperbolic n-manifold of finite volume. In particular, we show that if the curve satisfies certain natural geometric conditions, then the pushforward of the parameter measure on the...

We give a general method for deducing statistical limit laws in situations where rapid decay of correlations has been established. As an application of this method, we obtain new results for time-one maps of hyperbolic flows. In particular, using recent results of Dolgopyat, we prove that many classical limit theorems of probability theory, such as the central limit theorem, the law of the iter...

Direct quotations from business leaders can communicate to the wider public the latent state of their organization as well as the beliefs of the organization’s leaders. Candid quotes from business leaders can have dramatic effects upon the share price of their organization. For example, Gerald Ratner in 1991 stated that his company’s products were crap and consequently his company (Ratners) los...

Professor George Nuttall founded the Journal of Hygiene in 1901. With time, the journal attracted an increasing number of papers on parasitological subjects that promptedNuttall to found another journal, Parasitology, in 1908. He edited both journals until his sudden death in 1933, and indeed it is recorded that initially he personally took responsibility for the substantial costs of production...

Jachymski [ Proc. Amer. Math. Soc., 136 (2008), 1359-1373] gave modified version of a Banach fixed point theorem on a metric space endowed with a graph. In the present paper, (G, Φ)-graphic contractions have been de ned by using a comparison function and studied the existence of fixed points. Also, Hardy-Rogers G-contraction have been introduced and some fixed point theorems have been proved. S...

Some fixed point theorems and common fixed point theorem in Logarithmic convex structure areproved.