‎‎‎Recently Samet et al. introduced the notion of $alpha$-$psi$-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce $alpha$-$(psi,varphi)$-contractive mappings and stablish coincidence and common fixed point theorems for two mapping in complete metric spaces. We present some examples to illustrate our results. As application...

Unipotent flows are well-behaved dynamical systems. In particular, Marina Ratner has shown that the closure of every orbit for such a flow is of a nice algebraic (or geometric) form. After presenting some consequences of this important theorem, these lectures explain the main ideas of the proof. Some algebraic technicalities will be pushed to the background. Chapter 1 is the main part of the bo...

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

The main goal of this survey is the description of the fruitful interaction between Ergodic Theory and Number Theory via the study of two beautiful results: the first one by Ben Green and Terence Tao (about long arithmetic progressions of primes) and the second one by Noam Elkies and Curtis McMullen (about the distribution of the sequence {√n}mod 1). More precisely, during the first part, we wi...

Understanding and Controlling Crosstalk between Parallel Molecular Wires Matthew G. Reuter,* Gemma C. Solomon, Thorsten Hansen, Tamar Seideman, and Mark A. Ratner Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113, United States Nano-Science Center and Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø Denmark Department of Ch...

We classify all locally finite joinings of a horospherical subgroup action on Γ\G when Γ is a Zariski dense geometrically finite subgroup of G = PSL2(R) or PSL2(C). This generalizes Ratner’s 1983 joining theorem for the case when Γ is a lattice in G. One of the main ingredients is equidistribution of non-closed horospherical orbits with respect to the Burger-Roblin measure which we prove in a g...

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...

In this paper, some recent results established by Marin Borcut [M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math. 28, 2 (2012), 207--214] and [M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform. 21, 2 (2012), 135--142] are generalized and improved, with much sho...

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...