In this work, we show that if f is a uniformly continuous map defined over Polish metric space, then the set of f-invariant measures with zero entropy G δ $G_\delta$ (in weak topology). particular, generic f-periodic dense in measures. This settles conjecture posed by Sigmund (Trans. Amer. Math. Soc. 190 (1974), 285–299), which states an invariant measure topological dynamical system satisfies ...

Consider a nonlocal conservation where the flux function depends on convolution of solution with given kernel. In singular local limit obtained by letting kernel converge to Dirac delta one formally recovers law. However, recent counter-examples show that in general solutions equations do not this work we focus laws modeling vehicular traffic: case, is anisotropic. We that, under fairly assumpt...

The main purpose of this article is to offer some characterizations of $delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Si...

Let T be an orientation-preserving Lipschitz expanding map of the circle T. A pre-image selector is a map τ : T → T with finitely many discontinuities, each of which is a jump discontinuity, and such that τ (x) ∈ T(x) for all x ∈ T. The closure of the image of a pre-image selector is called a flower, and a flower with p connected components is called a p-flower. We say that a real-valued Lipsch...

In this paper‎, ‎using a generalized Dunkl translation operator‎, ‎we obtain a generalization of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the$(psi,p)$-Lipschitz Dunkl condition in the space $mathrm{L}_{p,alpha}=mathrm{L}^{p}(mathbb{R},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.  

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.