Cubic Structure on Soft Gamma-m-Normed Linear Space

Abstract

Objectives: The purpose of this research is to take the lead in comprehending the fuzzy idea of cubic structure on soft Gamma-m normed linear space. According to the theory of Soft m-Normed Linear Space (SMNLS), we offer the conviction of Cauchy's sequence and convergence in cubic Soft Gamma-m Normed Linear Space (CSGMNLS). We have obtained certain results like the concept of completeness in CSGMNLS. Methods: In this paper we defined the soft gamma ring, soft gamma ideals and soft gamma vector space which are used to introduce the notion of soft gamma-2-normed linear space, Soft Gamma-m-Normed Linear Space (SGMNLS) and its properties. Also, the CSGMNLS can be analyzed by using the SGMNLS. Findings: In this research from CSGMNLS construct a norm function that satisfies the properties of SGMNLS, and additionally given that example with proof in which a sequence is cauchy sequence and convergence in SGMNLS if it is cauchy and convergence sequence in CSGMNLS. Also, provided theorem and its proof for completeness of a sequence in CSGMNLS. Novelty: Already gamma ring and fuzzy n-normed linear space has been defined. We introduced the concept of SGMNLS using this also initiated the CSGMNLS and some results obtained from its properties. We suggested a necessary conditions for completeness of a sequence in CSGMNLS. Keywords: Soft Gamma ring, Soft gamma vector space, Soft gamma normed linear space, Soft m-norm, Soft m-normed linear space, 2-Normed and m-normed right soft gamma linear space