Tytuł artykułu
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Abstrakty
In this article, we study the best approximation in quotient probabilistic normed space. We define the notion of quotient space of a probabilistic normed space, then prove some theorems of approximation in quotient space are extended to quotient probabilistic normed space.
Wydawca
Czasopismo
Rocznik
Tom
Strony
53--57
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Department of Mathematics, National Institute of Technology, Silchar, Silchar 788010, India
autor
- Department of Mathematics, Silchar Polytechnic, Silchar 788015, Assam, India
autor
- Department of Mathematics, Tripura University, Suryamaninagar, Agartala 799022, Tripura, India
Bibliografia
- [1] M. Abrishami Moghaddam and T. Sistani, Best approximation in quotient generalised 2-normed spaces, J. Appl. Sci. 11 (2011), no. 16, 3039-3043.
- [2] C. Alsina, B. Schweizer and A. Sklar, On the definition of a probabilistic normed space, Aequationes Math. 46 (1993), 91-98.
- [3] I. Golet, On probabilistic 2-normed spaces, Novi Sad J. Math. 35 (2005), no. 1, 95-102.
- [4] S. Karakus, Statistical convergence on probabilistic normed spaces, Math. Commun. 12 (2007), 11-23.
- [5] B. Lafuerza-Guillén, D. O’regan and R. Saadati, Quotient probabilistic normed spaces and completeness results, Proc. Indian Acad. Sci. Math. Sci. 117 (2003), no. 1, 61-70.
- [6] H. Mazaheri and S. M. Moshtaghioun, Some results on p-best approximation in vector spaces, Bull. Iranian Math. Soc. 35 (2009), no. 1, 119-127.
- [7] K. Menger, Statistical metrices, Proc. Natl. Acad. Sci. USA 28 (1942), 535-537.
- [8] A. Pourmoslemi and M. Salimi, D-bounded sets in generalized probabilistic 2-normed spaces, World Appl. Sci. J. 3 (2008), no. 2, 265-268.
- [9] S. Rezapour, 2-proximinality in generalised 2-normed spaces, Southeast Asian Bull. Math. 33 (2009), 109-113.
- [10] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334.
- [11] A. N. Šerstnev, Random normed spaces: Problems of completeness, in: Probabilistic Methods and Cybernetics. I, Kazan University, Kazan (1962), 3-20.
- [12] M. Shams, S. M. Vaezpour and R. Saadati, p-best approximation on probabilistic normed spaces, Amer. J. Appl. Sci. 6 (2009), no. 1, 147-151.
- [13] I. Singer, Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Grundlehren Math. Wiss. 171, Springer, Berlin, 1970.
- [14] B. C. Tripathy and R. Goswami (2015), Vector valued multiple sequences defined by Orlicz functions, Bol. Soc. Parana. Mat. (3), to appear.
- [15] B. C. Tripathy, M. Sen and S. Nath (2012), I-convergence in probabilistic n-normed space, Soft Comput. 16 (2012), 1021-1027.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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