For a non-decreasing sequence of positive integers tending to infinity $\lambda=(\lambda_m)$ such that $\lambda_{m+1}-\lambda_m\leq 1$, $\lambda_1=1$; $(V,\lambda)$-summability has been defined as the limit generalized de la Val\'{e}e-Pousin sequence, [10]. In present research, we will establish some Tauberian, Abelian and Core Theorems related $(V,\lambda)$-summability.

We study a general class of Euclidean algorithms which compute the greatest common divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various tools of analytic combinatorics: generating functions, Dirichlet series, Taube...

Standard proofs of the ergodic theorems of demography rely on theorems borrowed from positive matrix theory, tauberian theory, and the theory of time-inhomogeneous Markov matrices. These proofs are efficient and expedient, but they give little direct insight into the mechanism that causes ergodicity. This paper proposes a simple and unified proof of the two ergodic theorems. It is shown that th...

The multiresolution expansion {Ejf}j∈N, f ∈ D Lq (R), 1 ≤ q ≤ ∞, is defined via a scaling function which order of regularity is equal to the order of f. Abelian and Tauberian type theorems for the quasiasymptotic behavior at infinity of distributions from D Lq (R) related to the quasiasymptotic behavior at infinity of its projections Ejf, j ∈ N, are given. AMS Mathematics Subject Classification...