arXiv subjects
Publications and source records attributed to Saeedeh Shamsi Gamchi.
In this paper, we prove that the topology induced by algebraic cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e. any algebraic cone metric space is metrizable. Furthermore, the notion of algebraic cone normed space is introduced and also normability of the topology of this space is proved.
In this paper the notion of modular cone metric space is introduced and some properties of such spaces are investigated. Also we define convex modular cone metric which takes values in CR(Y) where Y is a compact Hausdorff space. Then a fixed point theorem is proved for contractions in these spaces. Furthermore, we make a remark on paper [9] and it will be proved that their fixed point result in modular metric spaces is not true.
In this paper we introduce a generalization of Hilbert C-modules which are pre- Finsler module namely C-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on C-semi-inner product spaces.