Smoothness via Geometry of orthogonality functional using 2-norm derivatives
*Kallal PalCorresponding authorkpal_phd22@thapar.eduDepartment of MathematicsThapar Institute of Engineering and TechnologyPatiala, Punjab, 147004, India0009-0004-2627-7785View full profile → , Sumit Chandoksumit.chandok@thapar.eduDepartment of MathematicsThapar Institute of Engineering and TechnologyPatiala, Punjab, 147004, India0000-0003-1928-2952View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Mar 2025
- Published Online:
- 09 May 2026
- Article type:
- Review Article
- Language:
- EN
- Article no.:
- JIM-2383
- Pages:
- 1–15
Abstract
Keywords
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References
[1] M. Y. Abed, “New form of orthogonality in the real normed spaces,” J. Interdiscip. Math., vol. 25, no. 8, pp. 2579-2584 (2022).
[2] D. Amir, “Characterizations of inner product spaces,” Operator Theory, vol. 20 (1986).
[3] K. Anevska and R. Malceski, “Generalization of Parallelepiped Equality in 2-Normed Space,” Int. J. Pure Appl. Sci. Technol., vol. 22, pp. 41-49 (2014).
[4] Y. J. Cho, P. C. S. Lin, S. S. Kim, and A. Misiak, Theory of 2-inner product spaces. Nova Science Publishers (2001).
[5] R. C. Diminnie and A. G. White, “2-inner product spaces and Gâteaux partial derivatives,” Comment. Math. Univ. Carolin., vol. 16, pp. 115-119 (1975).
[6] R. Ehret, “Linear 2-Normed Spaces,” Ph.D. dissertation, Saint Louis Univ. (1969).
[7] S. Gähler, “Lineare 2-normierte Räume,” Math. Nachr., vol. 28, pp. 1-43 (1964).
[8] G. Godini, “MR0743643 (85g: 46028),” MathSciNet: Mathematical Reviews on the Web.
[9] H. Gunawan, Mashadi, S. Gemawati, and I. Sihwaningrum, “Orthogonality in 2-normed spaces revisited,” Publikacije Elektrotehničkog fakulteta, Ser. Mat., vol. 28, pp. 76-83 (2006).
[10] H. Gunawan, Mashadi, S. Gemawati, and I. Sihwaningrum, “On b-orthogonality in 2-normed spaces,” J. Indones. Math. Soc., vol. 16, no. 2, pp. 127-132 (2010).
[11] K. S. Ha, Y. J. Cho, and S. S. Kim, “Strictly convex linear 2-normed spaces,” Math. Nachr., vol. 146, pp. 7-16 (1990).
[12] A. Kundu, T. Bag, and S. Nazmul, “On metrizability and normability of 2-normed spaces,” Math. Sci., vol. 13, pp. 69-77 (2019).
[13] A. Khan and A. Siddique, “B-orthogonality in 2-normed spaces,” Bull. Calcutta Math. Soc., vol. 74, pp. 216-222 (1982).
[14] Y. Ma, “ρ-Orthogonality properties in 2-normed space,” Adv. Fixed Point Theory, vol. 12, pp. 1-12 (2022).
[15] H. Mazaheri and S. G. Nezhad, “Some results on b-orthogonality in 2-normed linear spaces,” Int. J. Math. Anal., vol. 1, pp. 681-687 (2007).
[16] P. M. Milicic, “Sur la g-orthogonalité dans un espace normé,” Q. J. Math., vol. 39, pp. 325-334 (1987).
[17] S. Rizvi and A. Siddiqui, “2-semi inner product spaces I,” Math. Japon., vol. 21, pp. 325-334 (1976).
[18] M. Nur and H. Batkunde, “A notion of Dg-orthogonality and Dg-angle in normed spaces,” J. Interdiscip. Math., vol. 27, no. 6, pp. 1285-1293 (2024).
[19] A. Zamani and M. S. Moslehian, “An extension of orthogonality relations based on norm derivatives,” Q. J. Math., vol. 70, pp. 379-393 (2019).
