A study involving the completion of quasi 2-normed space

The fundamental aim of this paper is to introduce and investigate a new property of quasi 2-normed space based on a question given by C. Park (2006) [2] for the completion quasi 2-normed space. Finally, we also find an answer for a question Park's.Comment: 7 page

Bounded and unbounded polynomials and multilinear forms: Characterizing continuity

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only if it transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the \emph{lineability} of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.Comment: 8 page

Bounded and Continuous Linear Operators on Linear 2-Normed Space

In this article, at first basic definitions and properties of linear 2-normed space are presented. Then the author defines bounded operator as an introduction to defined norm of an operator. In addition, the definition of continuous operator on a linear 2-normed space is given. This article proved an operator Γ from a linear 2-normed space (U,〖||.||〗_U) into a linear 2-normed space (V, 〖||.||〗_V) is bounded operator if and only if Γ is continuous operator