On soft refined 2-normed spaces
Authors
J. Sanabria
- Departamento de Matematicas, Facultad de Educacion y Ciencias, Universidad de Sucre, Sincelejo, Colombia.
O. Ferrer
- Departamento de Matematicas, Facultad de Educacion y Ciencias, Universidad de Sucre, Sincelejo, Colombia.
A. Sierra
- Centro de Ciencias Matematicas, Universidad Nacional Autonoma de Mexico, Mexico.
Abstract
In this work, we introduce the concepts of refined soft 2-normed spaces and refined soft 2-inner product spaces, obtaining important results such as Cauchy-Schwarz Inequality, that each refined soft 2-inner product induces a refined soft 2-normed space and that a refined soft 2-normed space is induced by a soft 2-inner product if the refined soft 2-normed satisfies the Parallelogram law. For this, we present the definition of refined linearly dependent soft vectors in a soft vector space which also allows us to show that given a classical inner product space, then the standard 2-inner product induces a refined soft 2-inner product space. The results presented here improve considerably the work of Kadhim [D. A. Kadhim, J. Al-Qadisiyah Comput. Sci. Math., \(\bf 6\) (2014), 157--168] and open a line of research in the context of refined soft 2-normed space and refined soft 2-inner product space.
Share and Cite
ISRP Style
J. Sanabria, O. Ferrer, A. Sierra, On soft refined 2-normed spaces, Journal of Mathematics and Computer Science, 37 (2025), no. 1, 1--19
AMA Style
Sanabria J., Ferrer O., Sierra A., On soft refined 2-normed spaces. J Math Comput SCI-JM. (2025); 37(1):1--19
Chicago/Turabian Style
Sanabria, J., Ferrer, O., Sierra, A.. "On soft refined 2-normed spaces." Journal of Mathematics and Computer Science, 37, no. 1 (2025): 1--19
Keywords
- Soft sets
- soft vectors
- soft linear space
- refined soft 2-normed space
- refined soft 2-inner product space
MSC
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