Operators reversing b-Birkhoff orthogonality in 2-normed linear spaces
الموضوعات :
1 - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
2 - Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
الکلمات المفتاحية: b-Birkhoff orthogonal, 2-functionals, 2-hyperplane, 2-inner product, 2-normed linear spaces,
ملخص المقالة :
In this paper, we discuss the relationships between 2-functionals and existence of b-Birkhoff orthogonal elements in 2-normed linear spaces. Moreover, we obtain some characterizations of 2-inner product spaces by b-Birkhoff orthogonality. Then we study the operators reversing b-Birkhoff orthogonality in 2-normed linear spaces.
[1] J. Alonso, H. Martini, S. Wu, On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces, Aequat. Math. 83 (2012), 153-189.
[2] J. Cho, S. S. Kim, Gateaux derivatives and 2-inner product spaces, Glas. Mat. (Ser. III). 27 (47) (1983), 197-203.
[3] J. Cho, P. C. S. Lin, S. S. Kim, A. Misiak, Theory of 2-Inner Product Spaces, Nova Science Publishies, New York, 2001.
[4] J. Cho, M. Matic, J. E. Pecaric, On Gram’s determinant in 2-inner product spaces, J. Korean Math. Soc. 38 (6) (2001), 1125-1156.
[5] C. R. Diminnie, A new orthogonality relation for normed linear spaces, Math. Nachr. 114 (1983), 197-203.
[6] S. S. Dragomir, J. Cho, S. S. Kim, A. Sofo, Some Boas-Bellman type inequalities in 2-inner product spaces, J. Ine. Pure. Appl. Math. (2005), 6(2):55.
[7] S. Gahler, Lineare 2-normierte R¨ aume, Math. Nachr. 28 (1965), 1-43.
[8] S. Kakutani, Some characterizations of Euclidean space, Japan. J. Math. 16 (1939), 93-97.
[9] A. Khan, A. Siddiqui, b-orthogonality in 2-normed space, Bull. Calcutta. Math. Soc. 74 (1982), 216-222.
[10] S. N. Lal, S. Bhattacharya, C. Sreedhar, Complex 2-normed linear spaces and extension of linear 2- functionals, J. Anal. Appl. 20 (1) (2001), 35-53.
[11] Z. Lewandowska, Generalized 2-normed spaces, Supskie Space Matemayczno Fizyczne. 1 (2001), 33-40.
[12] Z. Lewandowska, Linear operators on generalized 2-normed spaces, Bull. Math. Soc. Sci. Math. Roumanie. 42(90) (4) (1999), 353-368.
[13] Z. Lewandowska, On 2-normed sets, Glas. Mat. (Ser. III). 38(58) (2003), 99-110.
[14] R. Malceski, K. Anevska, About the 2-Banach spaces, Inter. J. Modern Engin. Res. 4 (5) (2014), 28-32.
[15] H. Mazaheri, S. Golestani Nezhad, Some results on b-orthogonality in 2-normed linear spaces, Int. J. Math. Anal. 14 (1) (2007), 681-687.
[16] S. A. Mohiuddin, Some new results on approximation in fuzzy 2-normed spaces, Math. Comput. Modelling. 53 (2011), 574-580.
[17] J. R. Partington, Orthogonality in normed spaces, Bull. Austral. Math. Soc. 33 (1986), 449-455.
[18] K. Singh, R. Kumar, 2-normed D-modules and Hahn-Banach theorem for D-linear 2-functionals, Fasc. Matematica. Tom XXIII (2) (2016), 117-126.
[19] T. Ta Swe, Bounded linear 2-functionals in linear 2-normed space, Dagon University Commemoration of 25th Anniversary Silver Jubilee Research Journal. 9 (2) (2019), 203-209.
