Completeness of Fuzzy Soft m-Normed Linear Space

Resumo

The aim of this research is to originate the hypothesis of fuzzy soft subspaces with its properties and fuzzy soft m-normed linear space, which is in accordance with the theory of fuzzy n-normed linear space and soft n-normed linear space. We presented formally the apprehension of fuzzy soft m-normed linear space and provided some results with examples of convergence sequences and Cauchy sequences in the fuzzy soft m-normed linear space. Methods: In this research paper we instituted the definition of fuzzy soft 2-normed linear space, fuzzy soft m-normed linear space, and its properties. The fuzzy soft m-normed linear space can be analyzed by using the fuzzy m-normed linear space and soft m-normed linear space. Findings: In this research paper, we construct the m-norm function that satisfies the properties of fuzzy soft m-normed linear space and provide the suitable example with proof, which is a convergence sequence and Cauchy sequence in fuzzy soft m-normed function if and only if it is a convergence sequence and Cauchy sequence in fuzzy soft m-normed linear space. Also proved a theorem for completeness of a sequence in fuzzy soft m-normed linear space. Novelty: We have well-defined definitions and theorems with proofs on fuzzy norms, fuzzy n-normed linear spaces, soft norms, and soft n-normed linear spaces. We established the abstraction of fuzzy soft m-normed linear space and gave results to theorems on properties of fuzzy soft m-normed linear space and also prepared necessary axioms for the completeness of a sequence in the fuzzy soft m-normed linear space.