Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.

abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.

We show that a multiplicative form of Dirichlet’s theorem on simultaneous Diophantine approximation as formulated by Minkowski, cannot be improved for almost all points on any analytic curve on R which is not contained in a proper affine subspace. Such an investigation was initiated by Davenport and Schmidt in the late sixties. The Diophantine problem is then settled via showing that certain se...

As a counterpart to best approximation, a new kind of approximation, called best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi. In this paper, we use this coapproximation to prove some results on the existence and uniqueness of best coapproximation in quotient spaces when the underlying spaces are metric linear spaces. We shall also see how coproximinality ...

Let N and P be smooth manifolds of dimensions n and p (n ≥ p ≥ 2) respectively. A smooth map having only fold singularities is called a fold-map. We will study conditions for a continuous map f : N → P to be homotopic to a fold-map from the viewpoint of the homotopy principle. By certain homotopy principles for fold-maps, we prove that if there exists a fiberwise epimorphism TN ⊕ θN → TP coveri...

Let X be a locally finite tree, and let G = Aut(X). Then G is a locally compact group. In analogy with Lie groups, Bass and Lubotzky conjectured that G contains lattices, that is, discrete subgroups whose quotient carries a finite invariant measure. Bass and Kulkarni showed that G contains uniform lattices if and only if G is unimodular and G\X is finite. We describe the necessary and sufficien...