King [3] introduced and examined the concepts of almost A-summable sequence, almost conservative matrix and almost regular matrix. In this paper, we introduce and examine the concepts of λ-almost A-summable sequence, λalmost conservative matrix and λ-almost regular matrix. Also we introduce statistically (V, λ)-summable sequence.

The compactness theorem is proved for sequences of functions that have estimates the higher derivatives in each subdomain domain definition, divided into parts by a sequence some curves class W_2^1. At same time, entire determining summable derivatives, these do not have. These results allow us to make limit transitions using approximate solutions problems with an unknown boundary describe proc...

This paper is concerned with singular matrix difference equations of mixed order. The existence and uniqueness initial value problems for these are derived, then the classification them obtained a similar classical Weyl's method by selecting suitable quasi-difference. An equivalent characterization this given in terms number linearly independent square summable solutions equation. influence off...

Abstract In this note, we deduce a strengthening of the Orlicz–Pettis theorem from Itô–Nisio theorem. The argument shows that given any series in Banach space which is not summable (or more generally unconditionally summable), can construct (coarse-grained) subseries with property that—under some appropriate notion “almost all”—almost all further thereof fail to be weakly summable. Moreover, by...

Given a sequence (Xn) of random variables, Xn is said to be near-record if Xn∈(Mn−1−a,Mn−1], where Mn=max{X1, …, Xn} and a>0 parameter. We investigate the point process η on [0,∞) values from an integer-valued, independent identically distributed sequence, showing that it Bernoulli cluster process. derive probability generating functional formulas for expectation, variance covariance countin...

The quantization dimension function for an F -conformal measure mF generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable Hölder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform a multifractal analysis, in our context of the m...

We present some new results on strongly summable ultrafilters. As the main result, we extend a theorem by N. Hindman and D. Strauss on writing strongly summable ultrafilters as sums.

Abstract Mixing rates, relaxation and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known non-summable variations. This paper exhibits upper bounds these quantities square-summable We obtain as corollaries a new block coupling inequality between pairs starting different histories. As applications our results, we prove weak i...