We have proved a theorem on |T, p n | k summability methods. This theorem includes a known theorem.

Let (un) be a sequence of real numbers and L be an additive summability method with some property. We show that if slow decrease of (un) or one-sided boundedness of the classical control modulo of the oscillatory behavior of (un) is a Tauberian condition for a general summability method L, then one-sided boundedness by a sequence with certain conditions of the general control modulo of the osci...

In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut − div ap(x,∇u) = f in ]0, T [×Ω with initial datum in L1(Ω) and assuming Dirichlet’s boundary condition, where ap(., .) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1(]0, T [×Ω) and Ω is a domain in RN . We find spaces of type Lr(0, T ;Mq(Ω)) containing ...

The classical summability methods of Borel (B) and Euler (E(λ), λ > 0) play an important role in many areas of mathematics. For instance, in summability theory they are perhaps the most important methods other than the Cesàro (Cα) and Abel (A) methods, and two chapters of the classic book of Hardy (1949) are devoted to them. In probability, the distinction between methods of Cesàro-Abel and Eul...

The theorems of Kozlov and Sullivan characterize Gibbs measures as with positive continuous specifications. More precisely, showed that every specification on symbolic configurations the lattice is generated by a norm-summable interaction. shift-invariant interaction satisfying weaker condition variation-summability. These results were proven in 1970s. An open question since time whether Kozlov...

Abstract The notion of statistical convergence was extended to $\mathfrak{I}$ I -convergence by (Kostyrko et al. in Real Anal. Exch. 26(2):669–686, 2000). In this paper we use such technique and introduce the statistically $\mathfrak{A}^{\mathfrak{I}}$ A -Cauchy $\mathf...

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.

A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.

In this paper we define double weighted generator sequence and prove some Tauberian theorems under which the convergence of bounded double sequences follows from its summability by weighted means. Mathematics Subject Classification 2010: 40C05, 40E05.

This article deals with some special cases which are extension of the strong summability of Fourier series with constant factor. We obtain a new equivalent form of inequalities A 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) φ (z) 2 dρ r/2 dθ ≤ B 2π 0 φ(e iθ) r dθ, (1) 2π 0 1 0 (1 − ρ) q−1 φ (z) q dρ r/q dθ ≤ C 2π 0 φ(e iθ) r dθ, (2) D 2π 0 φ(e iθ) r dθ ≤ 2π 0 1 0 (1 − ρ) p−1 φ (z) p dρ r/p dθ.