2-Semi-Bounded Linear Operators
DOI:
https://doi.org/10.29304/jqcm.2023.15.1.1150Keywords:
2-semi-Bounded operators, complete spaces, continuous and linear functionsAbstract
In this Article, we introduced a new definition of 2- semi bounded operator in 2- inner product space. Then, we investigate a new Space of bounded operators and proved it as vector space. After that we show this space as Banach space. Finally, we discussed some properties of this space.
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References
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A. Soenjaya, "On n-bounded and n-continuous operator in n-normed space," J. Indones. Math. Soc, vol. 18, no. 1, pp. 45-56, 2012.
R. Vijayaragavan, "Best approximation in real linear 2-normed spaces," IOSR journal of mathematics, vol. 6, no. 3, pp. 16-24, 2013.
Z. Lewandowska, "Bounded 2- Linear operators on 2- normed sets," Glasnik Mathematicki, vol. 39, pp. 303-314, 2004.
R. E. Megginson, An Introduction to Banach space Theory, New York: Springer, 1998.
H. GUNAWAN, "On Convergence in n-Inner Product Spaces," BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol. 25, pp. 11-16, 2002.
J. C. A. K.-G. GROSSE-ERDMANN, "SEQUENTIAL DEFINITIONS OF CONTINUITY FOR REAL FUNCTIONS," ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol. 33, no. 1, pp. 93-121, 2003.
S. Gahler, "Uber der Uniformisibrakeit2-metrische Raume," Math Nachr, vol. 28, no. 3-4, pp. 235-244, 1965.
R. Kazime, "Some Results on 2-inner product spaces," Novi Sad J. Math., vol. 37, no. 2, pp. 35-40, 2007.
L. K. Skaakir, A. S. Mohammed and A. A. Hijab, "Symmetric 2-normed spaces," Journal of interdisciplinary Mathematics, pp. 1-4, 2020.
S. H. Sababe, "On 2-Inner Product Spaces and Reproducing Kernel Property," Preprints, pp. 1-8, 2019.
Y. Cho, C. Diminnie, R. Freese and E. Andalafte, "Isosceles Orthogonal Triples in Linear 2-normed Spaces," Math. Nachr, vol. 157, pp. 225-234, 1992.
Y. Cho, P. Lin, S. Kim and A. Misiak, "Theory of 2-inner Product Spaces," in Nova Science Publishes Inc, New York, 2001.
C. Diminnie, S. Gahler and A. White, "2-inner Product spaces II," Demonstr.Math, vol. 10, pp. 169-188, 1977.
S. S. Dragomir, Y. Cho, S. S. Kim and A. Sofo, "Some Boas-Bellman Type Inequalities in 2-inner Product Spaces," J. Inequal. Pure Appl. Math, vol. 6, no. 2, pp. 1-13, 2003.
R. W. Freese and Y. J. Cho, "Geometry of linear 2-normed space," Nova science publisher, New York, 2001.
R. Freese and S. Gahler, "Remarks on Semi-2-normed Spaces," Math. Nachr, vol. 105, pp. 151-161, 1982.
S. Gozali and H. Gunawan, "On b-orthogonality in 2-normed Spaces," J. Indones. Math. Soc, vol. 16, pp. 127-132, 2009.
A. Misiak, "n-inner Product Spaces," Math. Nachr, vol. 140, no. 1, pp. 299-319, 1989.
P. Harikrishnan and K. Ravindran, "Some properties of accretive operators in linear 2-normed space," International Mathematical Forum,, vol. 6, no. 59, pp. 2941-2947, 2011.
J. R. Giles, "Introduction to the analysis of normed linear spaces," Cambridge university press, New York, 2000.
A. Soenjaya, "On n-bounded and n-continuous operator in n-normed space," J. Indones. Math. Soc, vol. 18, no. 1, pp. 45-56, 2012.
R. Vijayaragavan, "Best approximation in real linear 2-normed spaces," IOSR journal of mathematics, vol. 6, no. 3, pp. 16-24, 2013.
Z. Lewandowska, "Bounded 2- Linear operators on 2- normed sets," Glasnik Mathematicki, vol. 39, pp. 303-314, 2004.
R. E. Megginson, An Introduction to Banach space Theory, New York: Springer, 1998.
H. GUNAWAN, "On Convergence in n-Inner Product Spaces," BULLETIN of the MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol. 25, pp. 11-16, 2002.
J. C. A. K.-G. GROSSE-ERDMANN, "SEQUENTIAL DEFINITIONS OF CONTINUITY FOR REAL FUNCTIONS," ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol. 33, no. 1, pp. 93-121, 2003.
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Published
2023-03-02
How to Cite
Azeez, A. M., & Shaakir, L. K. (2023). 2-Semi-Bounded Linear Operators. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(1), Math Page 46–51. https://doi.org/10.29304/jqcm.2023.15.1.1150
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Math Articles
