In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an $n$-normed space, we are interested in bounded multilinear $n$-functionals and $n$-dual spaces. The concept of bounded multilinear $n$-functionals on an $n$-normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear $n$-functionals, introduce the concept of $n$-dual...

Given a free ultrafilter $p$ on $\mathbb{N}$ and a space $X$, we say that $x\in X$ is the $p$-limit point of a sequence ${\left(x_n\right)}_{n\in \mathbb{N}}$ in $X$ (in symbols, $x=p$-${lim}_{n\to \infty }{x}_n$) if for every neighborhood $V$ of $x$, $\{n\in \mathbb{N}:x_n\in V\}\in p$. By using $p$-limit points from a suitable metric space, we characterize the selective ultrafilters on $\mathbb{N}$ and the $P$-points of ${\mathbb{N}}^{*}=\beta \left(\mathbb{N}\right)\setminus \mathbb{N}$. In this paper, we only consider dynamical systems $(X,f)$, where $X$ is a compact metric space. For a free ultrafilter $p$ on ${\mathbb{N}}^{*}$, the function $f^p:X\to X$ is defined by $f^p\left(x\right)=p$-${lim}_{n\to \infty }{f}^n\left(x\right)$ for each $x\in X$. These functions are not continuous in general....

In this note we investigate the relationship between the convergence of the sequence $\left\{S_n\right\}$ of sums of independent random elements of the form $S_n={\sum }_{i=1}^n{\epsilon }_i{x}_i$ (where ${\epsilon }_i$ takes the values $\pm 1$ with the same probability and $x_i$ belongs to a real Banach space $X$ for each $i\in \mathbb{N}$) and the existence of certain weakly unconditionally Cauchy subseries of ${\sum }_{n=1}^{\infty }{x}_n$.