A summability factor theorem for absolute summability involving quasi-monotone sequences

In this paper we prove a theorem on _|A|k,k≥1${\left|A\right|}_k,k\ge 1$, summability factors for an infinite series by replacing a weighted mean matrix with a triangular matrix.     

On the generalized absolute summability factor theorem

In this paper, we establish a summability factor theorem for summability _|A|k${\left|A\right|}_k$ where A$A$ is a lower triangular matrix with non-negative entries satisfying certain conditions.     

Double absolute summability factor theorems and applications

In an earlier paper the first author [Ekrem Savas, Factors for _|A|k${\left|A\right|}_k$ summability of infinite series, Comput. Math. Appl. 53 (7) (2007) 1045–1049. [3]] obtained a summability factor theorem for absolute summability of the order k≥1$k\ge 1$. In this paper we extend that result to doubly infinite matrices.     

A study on absolute Riesz summability factors

In the present paper, two general theorems on summability factors of infinite series which generalize some known results, have been proved. Also we have obtained two new results concerning the |C,1;δ| _k summability factors.     

Quasi-power increasing sequence for generalized absolute summability

In this paper, we prove a theorem given in [E. Sava?, On almost increasing sequences for generalized absolute summability, Math. Inequal. Appl., Preprint] on summability factors under weaker conditions by using a quasi-β$\beta$-power increasing sequence instead of an almost increasing sequence.     

On generalized absolute summability factors

In this paper, a general theorem on _|A,δ|k${|A,\delta |}_k$-summability factors which generalize a theorem of Sava? [E. Sava?, On a recent result on absolute summability factors, Appl. Math. Lett. 18 (2005) 1273–1280] on _|A|k${\left|A\right|}_k$-summability factors has been proved.     

A study on weighted mean summability

In the present paper, a general theorem on summability factors of infinite series has been proved. Also we have obtained a new result concerning the |C,1;δ| _k summability factors.     

Almost sure Cesàro and Euler summability of sequences of dependent random variables

For a sequence of real random variables C _α-summability is shown under conditions on the variances of weighted sums, comprehending and sharpening strong laws of large numbers (SLLN) of Rademacher-Menchoff and Cramér-Leadbetter, respectively. Further an analogue of Kolmogorov’s criterion for the SLNN is established for E _α-summability under moment and multiplicativity conditions of 4th order, which allows one to weaken Chow’s independence assumption for identically distributed square integrable random variables. The simple tool is a composition of Cesàro-type and of Euler summability methods, respectively. Received: 12 June 2006, Revised: 14 May 2007     

Existence of solutions to some retarded integrodifferential equations via the topological transversality theorem

We prove the existence of solutions to some retarded integrodifferential equations under some suitable conditions on the involved functions. Some applications of our results are also provided.     

A new rating system for duplicate bridge

We propose a new way to rate individual duplicate bridge players, which we believe is superior to the masterpoint system currently used by the American Contract Bridge League. This method measures only a player’s current skill level, and not how long or how frequently he has played. It is based on simple ideas from the theory of statistics and from linear algebra, and should be easy to implement.One particular issue which can occur within any system proposing to rate individual players using results earned by partnerships is what we call the “nonuniqueness problem”. This refers to the occasional inability for data to distinguish who is the “good player” and who is the “bad player” within particular partnerships. We prove that under our system this problem disappears if either (a) a certain “partnership graph” has no bipartite components, or if (b) every player is required to participate in at least one individual game.Finally, we present some data from a bridge club in Reno, NV. They show that even if (a) and (b) do not hold, our system will provide (unique) ratings for most players.     

A limit theorem for the time of ruin in a Gaussian ruin problem

For certain Gaussian processes X(t)$X\left(t\right)$ with trend −ct^β$-c{t}^{\beta }$ and variance V²(t)$V^2\left(t\right)$, the ruin time is analyzed where the ruin time is defined as the first time point t$t$ such that X(t)−ct^β≥u$X\left(t\right)-c{t}^{\beta }\ge u$. The ruin time is of interest in finance and actuarial subjects. But the ruin time is also of interest in other applications, e.g. in telecommunications where it indicates the first time of an overflow. We derive the asymptotic distribution of the ruin time as u→∞$u\to \infty$ showing that the limiting distribution depends on the parameters β$\beta$, V(t)$V\left(t\right)$ and the correlation function of X(t)$X\left(t\right)$.     

Concavity and sharp inequalities for a recursive sequence arising in game theory

This paper is concerned with the sequence q(n) recursively defined as q(2) = ¼ and

     

A Dunkl-Williams type inequality for absolute value operators

Dunkl and Williams showed that for any nonzero elements x,y in a normed linear space X

     

Lower bounds of Copson type for Hausdorff matrices

Let 1 ? p ? ∞, 0 < q ? p, and A = (a_n,k)_n,k?0 ? 0. Denote by L_p,q(A) the supremum of those L satisfying the following inequality: