New inner product quasilinear spaces on interval numbers (Q739907)

Summary: Primarily we examine the new example of quasilinear spaces, namely, ``\(I \mathbb{R}^n\) interval space.'' We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results on \(I \mathbb{R}^n\) interval space related to these concepts. Secondly, we present \(I s, I c_0, I l_{\infty}\), and \(I l_2\) quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.