Article Sidebar

Submitted
May 9, 2023
Accepted
December 2, 2023
Published
November 30, 2023
Download
PDF
Statistic
Read Counter : 268 Download : 370

Downloads

Download data is not yet available.

Main Article Content

Abstract

Given an n-normed space X for n>= 2$, we investigate the completness of Y (as subspace of X) respect to a new norm that corresponds this new inner product on Y. Moreover, we discuss the angle between two subspaces in Y.

Keywords

n-norm completness inner product angles

Article Details

Creative Commons License

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

How to Cite
Nur, M., & Idris, M. . (2023). A New Notion of Inner Product in A Subspace of n-Normed Spaces. Journal of the Indonesian Mathematical Society, 29(3), 372–381. https://doi.org/10.22342/jims.29.3.1412.372-381
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. V. Balestro, A.G. Horv`ath, H. Martini, and R. Teixeira, Angles in normed spaces, ` Aequationes
  2. Math., 91(2) (2017), 201-236.
  3. H. Batkunde, and H. Gunawan, A revisit to n-normed spaces through its quotient spaces,
  4. Matematychni Studii 53(2) (2020), 181-191.
  5. R. Benitez, Carlos Orthogonality in normed linear spaces: a classification of the different
  6. concepts and some open problems, Revista Mathematica 2 (1989) 53-57.
  7. S. G¨ahler, Lineare 2-normierte r¨aume, Math. Nachr. 28 (1964), 1-43.
  8. S. G¨ahler, Untersuchungen ¨uber verallgemeinerte m-metrische R¨aume. I, Math. Nachr. 40
  9. (1969), 165-189.
  10. S. G¨ahler, Untersuchungen ¨uber verallgemeinerte m-metrische R¨aume. II, Math. Nachr. 40
  11. (1969), 229-264.
  12. J. R. Giles, Classes of semi-inner-product spaces,Trans. Amer. Math. Soc. 129(3) (1967),
  13. -446.
  14. H. Gunawan, On n-inner products, n-norms, and the Cauchy-Schwarz inequality, Sci. Math.
  15. Jpn. 55 (2002), 53-60.
  16. H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27 (2001),
  17. -329.
  18. H. Gunawan, O. Neswan, and W. Setya-Budhi, A formula for angles between two subspaces
  19. of inner product spaces, Beitr. Algebra Geom., 46(2) (2005), 311-320
  20. H. Gunawan, O. Neswan, and E. Sukaesih, Fixed point theorems on bounded sets in an
  21. n-normed space, J. Math. Comput. Sci., 8(2) (2018), 196-215.
  22. H. Gunawan and O. Neswan, On angles between subspaces of inner product spaces, J. Indo.
  23. Math. Soc., 11 (2005), 129-135.
  24. M. Idris , S. Ekariani and H. Gunawan, On the space of p-summable sequences, Mat. Vesnik.,
  25. (1) (2013), 58-63.
  26. R.C. James, Orthogonality in normed linear spaces, Duke Math. J. 12, (1945) 291-302.
  27. S. Konca, M. Idris, and H. Gunawan, p-summable sequence spaces with inner products, Beu
  28. J. Sci. Techn., 5(1) (2015), 37-41.
  29. E. Kreyszig, Introductory Functional Analysis with Applications, John Wiley & Sons, Inc.,
  30. New York, 1978.
  31. A.L. Soenjaya, On n-bounded and n-continuous operator in n-normed space, Journal of the
  32. Indonesian Mathematical Society, 18(1) (2012), 45-56.
  33. P. M. Mili`ci`c, On the B-angle and g-angle in normed spaces, J. Inequal. Pure Appl. Math.,
  34. (3) (2007), 1-9.
  35. A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319.
  36. M. Nur, M. Idris and Firman, Angle in the space of p-summable sequences, AIMS Mathematics, 7(2) (2022), 2810-2819.
  37. M. Nur, and H. Gunawan, A new orthogonality and angle in a normed space, Aequationes
  38. Math. 93 (2019), 547-555.
  39. M. Nur, and H. Gunawan, A note on the g-angle between subspaces of a normed space,
  40. Aequationes Math., 95 (2021), 309-318