On soft linear spaces and soft normed linear spaces
Sujoy Das, Pinaki Majumdar, S. K. Samanta
TL;DR
This paper introduces the concepts of soft linear spaces and soft normed linear spaces, exploring their properties, completeness, and the relationships between different soft norms and convex soft sets.
Contribution
It presents new definitions and properties of soft linear and soft normed linear spaces, including soft vectors, completeness, and equivalence of soft norms.
Findings
Soft vectors and their properties are characterized.
Completeness of soft normed linear spaces is established.
Equivalence of soft norms and properties of convex soft sets are analyzed.
Abstract
In this paper an idea of soft linear spaces and soft norm on soft linear spaces are given and some of their properties are studied. Soft vectors in soft linear spaces are introduced and their properties are studied. Completeness of soft normed linear space is also studied and equivalent soft norms and convex soft sets are studied in soft normed linear space settings.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Algebra and Logic · Fixed Point Theorems Analysis