We show that a real bounded sequence (xn) is Cesaro convergent to l if and only the of averages with indices in [αk,αk+1) converges for all α>1 . If, addition, (xn)...

In this paper, the long-time behavior of Cesaro mean fundamental solution for fractional Heat equation corresponding to random time changes in Brownian motion is studied. We consider both stable subordinators leading equations with Caputo-Djrbashian derivative and more general cases differential-convolution operators, particular, distributed order derivatives.

We analyze a routing scheme for a broad class of networks which converges (in the Cesaro sense) with probability one to the set of approximate Cesaro–Wardrop equilibria, an extension of the notion of a Wardrop equilibrium. The network model allows for wireline networks where delays are caused by flows on links, as well as wireless networks, a primary motivation for us, where delays are caused b...

On the OrliczCesaro sequence spaces ( ces ) which are defined by using Orlicz function , we show that the space ces equipped with both Amemiya and Luxemburg norms possesses uniform Opial property and uniform Kadec-Klee property if satisfy the 52 -condition.

The Zhao-Woodroofe condition has been introduced in [19] and it is a necessary and sufficient condition for the existence of a martingale approximation of a causal stationary process. Here, a nonadapted version is given and the convergence of Cesaro averages is replaced by a convergence of a subsequence. The nonadapted version is of a different form than in other cases, e.g. of Wu-Woodroofe or ...

It is well known that (see [9]) Cesaro means of 2π-periodic functions f ∈ Lp(T) (1 ≤ p ≤ ∞) converges by norms. Hereby T is denoted the interval (−π,π). The problem of the mean summability in weighted Lebesgue spaces has been investigated in [6]. A 2π-periodic nonnegative integrable function w : T→R1 is called a weight function. In the sequel by L p w(T), we denote the Banach function space of ...