On Paranormed and Locally Convex Quasilinear Spaces
Konuralp Journal of Mathematics, cilt.14, sa.1, ss.185-194, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 1
- Basım Tarihi: 2026
- Dergi Adı: Konuralp Journal of Mathematics
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.185-194
- Anahtar Kelimeler: Locally convex quasilinear space, Paranormed quasilinear space, Quasilinear space
- İnönü Üniversitesi Adresli: Evet
Özet
The concept of a normed quasilinear space was defined by Aseev in [1]. Based on this concept, topological quasilinear spaces are given in [5] and their properties are analysed. Definition of seminormed quasilinear spaces based on these definitions was given in [8] and their topological structure is analysed in this reference. In this paper, we introduce paranormed and locally convex quasilinear spaces and give some examples. We observe that every normed quasilinear space is a paranormed quasilinear space. Finally we prove that the topology of a locally convex quasilinear space comes from a family of seminorms which are defined on the quasilinear space.