Some properties of \(b\)-linear functional in linear \(n\)-normed space

Downloads

DOI:

https://doi.org/10.26637/mjm1004/008

Abstract

Some results in linear \(n\)-normed space have been discussed. Several nice properties of bounded \(b\)-linear functional in linear \(n\)-normed space are presented. We see that the collection of all bounded \(b\)-linear functionals after introducing suitable operations, is a normed space.

Keywords:

hyperplane, convex set, sequentially continuous, \(n\)-normed space , \(b\)-linear functional , \(n\)-Banach space

Mathematics Subject Classification:

46A22, 46A32, 46B07, 46B25
  • Prasenjit Ghosh Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata, 700019, West Bengal, India
  • T.K. Samanta Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata, 700019, West Bengal, India.
  • Pages: 374-385
  • Date Published: 01-10-2022
  • Vol. 10 No. 04 (2022): Malaya Journal of Matematik (MJM)

R. Freese, Y. J. Cho, Geometry of Linear 2-normed Spaces, Nova Science Publishers,New York (2001).

P. Ghosh, T. K. Samanta, Representation of uniform boundedness principle and Hahn-Banach theorem in linear n-normed space, DOI https://doi.org/10.1007/s41478-021-00358-x.

P. Ghosh, T. K. Samanta, Reflexivity of linear n-normed space with respect to b-linear functional, Submitted, arXiv: 2101.09661.

P. Ghosh, S. Roy and T. K. Samanta, Uniform boundedness principle and Hahn-Banach theorem for $b$ linear functional related to linear 2-normed space, South East Asian J. of Mathematics and Mathematical Sciences, Vol. 16, No. 2 (2020), pp. 131-150.

S. Gahler, Lineare 2-normierte raume, Math. Nachr. 28 (1964), 1-43.

H. Gunawan, Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27, 2001, 631-639.

P. K. Jain, O. P. Ahuja, Functional Analysis, New Age International Publisher, 1995.

A. L. Soenjaya, The Open Mapping Theorem in n-Banach space, International Journal of Pure and Applied Mathematics, Vol. 76, No. 4, 2012, 593-597.

A. White, 2-Banach spaces, Math. Nachr., 42 (1969), 43–60.

  • NA

Metrics

Metrics Loading ...

Published

01-10-2022

How to Cite

Ghosh, P., and T. . Samanta. “Some Properties of \(b\)-Linear Functional in Linear \(n\)-Normed Space”. Malaya Journal of Matematik, vol. 10, no. 04, Oct. 2022, pp. 374-85, doi:10.26637/mjm1004/008.

Issue

Vol. 10 No. 04 (2022): Malaya Journal of Matematik (MJM)

Section

Articles

License

Copyright (c) 2023 Prasenjit Ghosh, T.K. Samanta

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC