Convergence of certain cosine sums in a metric space ―\ $L$

Some New Modified Cosine Sums and L1-convergence of Cosine Trigonometric Series

In this paper we introduce some new modified cosine sums and then using these sums we study L1-convergence of trigonometric cosine series.

On the convergence of certain sums of independent random elements

Our notation is standard ([1], [3], [4], [9]). Throughout this note ∆ will denote the Cantor space {−1, 1}, Σ the σ-algebra of subsets of ∆ generated by the n-cylinders of ∆ for each n ∈ N, and ν the Borel probability ⊗i=1νi on Σ, where νi : 2 {−1,1} → [0, 1] is defined by νi(∅) = 0, νi({−1}) = νi({1}) = 1/2 and νi({−1, 1}) = 1 for each i ∈ N. In what follows X will be a real Banach space and L...

Sums of an Entire Function in Certain Weighted L-spaces

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...

Convergence of Fourier Series in L Space

The convergence of Fourier series of trigonometric functions is easy to see, but the same question for general functions is not simple to answer. We study the convergence of Fourier series in Lp spaces. This result gives us a criterion that determines whether certain partial differential equations have solutions or not.We will follow closely the ideas from Schlag and Muscalu’s Classical and Mul...