A Note on Spătaru's Complete Convergence Theorem

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

A note on convergence in fuzzy metric spaces

The sequential $p$-convergence in a fuzzy metric space, in the sense of George and Veeramani, was introduced by D. Mihet as a weaker concept than convergence. Here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. In such a case $M$ is called an $s$-fuzzy metric. If $(N_M,ast)$ is a fuzzy metri...

A Note on Subseries Convergence

A Note on Multigrid Convergence

We generalise the abstract V-cycle convergence proof of 20] and 21] to include unsymmetricsmoothing operations as well. In the case of full regularity we obtain better convergence with an increasing number of smoothing steps, thus recovering the results of 2]. Applying our theory to an anisotropic model problem we obtain optimal results in this case as well.

A note on Pollard’s Theorem

Let A,B be nonempty subsets of a an abelian group G. Let Ni(A,B) denote the set of elements of G having i distinct decompositions as a product of an element of A and an element of B. We prove that ∑ 1≤i≤t |Ni(A,B)| ≥ t(|A|+ |B| − t− α+ 1 + w) − w, where α is the largest size of a coset contained in AB and w = min(α − 1, 1), with a strict inequality if α ≥ 3 and t ≥ 2, or if α ≥ 2 and t = 2. Thi...