New inner product quasilinear spaces on interval numbers

Aseev [2] launched a new branch of functional analysis by introducing the concept of quasilinear spaces which is generalization of classical linear spaces. He proceeds, in a similar way to linear functional analysis on quasilinear spaces by introducing the notions of norm, with quasilinear operators and functional. We know that any inner product space is a normed space and any normed space is a particular class of normed quasilinear space. Hence, this relation and Aseev’s work motivated us to quasilinear counterparts of inner product space in classical analysis in [7]. Generally in [7], we give some consistent quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. In this work, we examine a new type of a quasilinear space, namely, “ ” interval space. We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependenceindependence and basis on quasilinear functional analysis [5], we obtain some results on “ ” interval space related to these concepts. Furthermore, we present the concepts of “ and ” interval sequence spaces as new examples of quasilinear spaces. Moreover, we obtain some theorems and results related to these new spaces which provide us with improving the elements of the quasilinear functional analysis.