We consider continuous, translation-commuting transformations of compact, translation-invariant families of mappings from finitely generated groups into finite alphabets. It is well-known that such transformations and spaces can be described “locally” via families of patterns and finitary functions; such descriptions can be re-used on groups larger than the original, usually defining non-isomor...

In this paper we prove a theorem giving sufficient conditions for the existence of common fixed points of pointwise R-subweakly commuting mappings on nonconvex sets. We apply this theorem to derive some results on the existence of common fixed points from the set of best approximation for this class of maps in the set up of metric spaces. The results proved in the paper generalize and extend so...

This is a topological dynamics perspective on the full bifurcation unfolding in unimodal mappings. We present a bundle structure, visualized as a bundle plot, to show the evolution of symbolic space as we vary a system parameter. The bundle plot can be viewed as a limit process of an assignment plot, which are lines assignments between points from two dynamical systems. Such line assignments ar...

As a natural generalization of various investigations in different function spaces, we study the following problem. Let A be an arbitrary set, and Tj (j = 1, . . . , n) be arbitrary commuting mappings – transformations – from A into A. Under what conditions can we state that a function f : A → A is the sum of “periodic”, that is, Tj-invariant functions fj? (A function g is periodic, i.e., invar...

In this paper we study commuting families of holomorphic mappings in Cn which form abelian semigroups with respect to their real parameter. Linearization models for holomorphic mappings are been used in the spirit of Schröder’s classical functional equation. The one-dimensional linearization models for holomorphic mappings and semigroups, based on Schröder’s and Abel’s functional equation have ...

Let C be a nonempty bounded closed convex subset of a complete CAT 0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k 1 defined by xk 1 1 − tmk xk ⊕ tmkT nk m y m−1 k, y m−1 k 1 − t m−1 k xk ⊕ t m−1 kT m−1y m−2 k, y m−2 ...

Active commuting could contribute to increasing physical activity. The objective of this study was to characterise patterns of active commuting to and from schools in children and adolescents in Chile. A total of 453 Chilean children and adolescents aged between 10 and 18 years were included in this study. Data regarding modes of commuting and commuting distance was collected using a validated ...

The present paper deals with some fixed point theorems for a class of mixed typeof contraction maps possessing the asymptotically regular property in a 2-Banach space.Full text References[1] M.Açıkgöz, A review on 2-normed structures, Int. Journal of Math. Analysis,1(2007), no.4, 187 191. MR2340939 (2008e:46012) Zbl 1132.46304.[2] Y.J.Cho, M.S.Khan and S.L.Sing, Common fixed...