We consider left permutive cellular automata Φ with no memory and positive anticipation, defined on the space of all doubly infinite sequences with entries from a finite alphabet. For each such automaton that is not one-to-one, there is a dense set of points x, which is large in another sense too, such that Φ : cl{Φn(x) : n ≥ 0} → cl{Φn(x) : n ≥ 0} is topologically conjugate to an odometer, the...

banach contraction principle has been generalized in different spaces by mathematicians over the years. mustafa and sims [18] proposed a new class of generalized metric spaces, which are called as g-metric spaces. in this type of spaces a non-negative real number is assigned to every triplet of elements. many mathematicians studied extensively various results on g-metric spaces by using the con...

Let H(d) be the space of complex hermitian matrices of size d×d and let H+(d) ⊂ H(d) be the cone of positive semidefinite matrices. A linear operator Φ : H(d1) → H(d2) is said to be positive if Φ[H+(d1)] ⊂ H+(d2). The concurrence C(Φ; ·) of a positive operator Φ : H(d1) → H(d2) is a real-valued function on the cone H+(d1), defined as the largest convex function which coincides with 2 q σ d2 2 (...

We define an analogue of the Caldero-Chapoton map ([CC]) for the cluster category of finite dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character (in the sense of [Pa]) and satisfies some inductive formulas for the multiplication between the generalized cluster variables (the images of objects of the cluster category under the map). Moreover, we con...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...