konuralp j. math.

Konuralp Journal of Mathematics

2147-625X

Mehmet Zeki SARIKAYA

Applied Mathematics (Other)

Uygulamalı Matematik (Diğer)

On Paranormed and Locally Convex Quasilinear Spaces

https://orcid.org/0000-0003-1484-782X

Yılmaz

Inonu University

https://orcid.org/0009-0005-7816-3357

Elmuhammed

Mahir

Inonu University

https://orcid.org/0000-0002-1673-3319

Yalçın

Seçkin

Inonu University

04 30 2026

14 1 185 194 05 16 2025 02 12 2026

2013

Konuralp Journal of Mathematics

The concept of a normed quasilinear space was dened by Aseev in [1]. Based on this concept, topological quasilinear spaces are given in [5] and their properties are analysed. Denition of seminormed quasilinear spaces based on these denitions was given in [8] and their topological structure is analysed in this reference. In this paper we will introduce paranormed and locally convex quasilinear spaces and will give some examples. We observe that every normed quasilinear space is a paranormed quasilinear space. Finall we will prove that the topology of a locally convex quasilinear space comes from a family of seminorms which are dened on the quasilinear space.

Quasilinear space Paranormed quasilinear space Locally convex quasilinear space

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