We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...

Let S be a semigroup. In certain cases we give some characterizations of extreme amenability of S and we show that in these cases extreme left amenability and extreme right amenability of S are equivalent. Also when S is a compact topological semigroup, we characterize extremely left amenable subalgebras of C(S), where C(S) is the space of all continuous bounded real valued functions on S

and Applied Analysis 3 It is an interesting problem to extend the above results to a strongly continuous semigroup of nonexpansive mappings and a strongly continuous semigroup of asymptotically nonexpansive mappings. Let S be a strongly continuous semigroup of nonexpansive self-mappings. In 1998 Shioji and Takahashi 11 introduced, in Hilbert space, the implicit iteration

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable mod...

We study the strong continuity of weighted composition semigroups of the form Ttf = φ′t (f ◦ φt) in several spaces of analytic functions. First we give a general result on separable spaces and use it to prove that these semigroups are always strongly continuous in the Hardy and Bergman spaces. Then we focus on two non-separable family of spaces, the mixed norm and the weighted Banach spaces. We...

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence  ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize thei...

We consider the special Jin-Xin relaxation model (0.1) ut + A(u)ux = 2(uxx − utt), We assume that the initial data (u0, 2u0,t) are sufficiently smooth and close to (ū, 0) in L∞ and have small total variation. Then we prove that there exists a solution (u2(t), 2ut(t)) with uniformly small total variation for all t ≥ 0, and this solution depends Lipschitz continuously in the L1 norm w.r.t. the in...

A generalized Mehler semigroup (Ornstein-Uhlenbeck semigroup) associated with some strongly continuous semigroup of linear operators on a real separable Hilbert space may be defined by using a skew convolution semigroup. Under a mild moment assumption, it is proved that the characteristic functional of any centered skew convolution semigroup is absolutely continuous and characterizations are gi...

Given continuous functions M and N of two variables, it is shown that if in a continuous iteration semigroup with only (M,N)-convex or (M,N)-concave elements there are two (M,N)-affine elements, then M = N and every element of the semigroup is M -affine. Moreover, all functions in the semigroup either are M -convex or M -concave.

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...