It is known that, for a positive Dunford-Schwartz operator in noncommutative L p -space, 1 ? < ? , or, more generally, Orlicz space with order continuous norm, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these blaterally uniformly each symmetric E such ? t ( x ) ? 0 as every ? where non-increasing rearrangement of . Noncommutative Dunford-Schwartz-type...

For any h ∈ N, a graph G = (V, E) is said to be h-magic if there exists a labeling l : E(G) → Zh−{0} such that the induced vertex labeling l+ : V (G) → Zh defined by l(v) = ∑ uv∈E(G) l(uv) is a constant map. When this constant is 0 we call G a zero-sum h-magic graph. The null set of G is the set of all natural numbers h ∈ N for which G admits a zero-sum h-magic labeling. A graph G is said to be...

In this paper, we obtained the convergence of modified Noor iterative scheme for nearly Lipschitzian maps in real Banach spaces. Our results contribute to the literature in this area of re- search.

We prove uniform convexity of solutions to the capillarity boundary value problem for fixed boundary angle in (0, π/2) and strictly positive capillarity constant provided that the base domain Ω ⊂ R is sufficiently close to a disk in a suitable C-sense.

We introduce a Halpern-type iteration for a generalized mixed equilibrium problem in uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are also established in this paper. As applications, we apply our main result to mixed equilibrium, generalized equilibrium, and mixed variational inequality problems in Banach spaces. Finally, examples and numerical results are al...

We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.

We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a ...

We consider the system of N (≥ 2) elastically colliding hard balls with masses m1, . . . , mN , radius r, moving uniformly in the flat torus T ν L = R /L · Z , ν ≥ 2. It is proved here that the relevant Lyapunov exponents of the flow do not vanish for almost every (N + 1)-tuple (m1, . . . , mN ;L) of the outer geometric parameters.

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

We prove that Hilbert geometries on uniformly convex Euclidean domains with C 2-boundaries are roughly isometric to the real hyperbolic spaces of corresponding dimension.