Best Coapproximation in Fuzzy Anti-n-Normed Spaces
The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets.
[1] T. Bag and T. K. Samanta, A comparative study of fuzzy norms on a
linear space, Fuzzy Sets and Systems. 159 (2008) 670 -684.
[2] C. Franchetti and M. Furi, Some characteristic properties of real Hilbert
spaces, Rev. Roumaine Math. Pures Appl. 17 (1972) 1045 - 1048.
[3] S. G¨ahler, Lineare 2-normierte R¨aume, Math. Nachr. 28 (1964) 1-43.
[4] S. G¨ahler and Unter Suchyngen U¨ ber Veralla gemeinerte m-metrische
R¨aume I, Math. Nachr. 40 (1969) 165 - 189.
[5] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math & Math.
Sci. 27(10) (2001) 631 - 639.
[6] Iqbal H. Jebril and T. K. Samanta, Fuzzy anti-normed space, J.
Mathematics and Technology, February (2010) 66 -77.
[7] A. K. Katsaras, Fuzzy topological vector spaces, Fuzzy Sets and Systems,
12 (1984) 143 - 154.
[8] J. Kavikumar, Y. B. Jun and Azme Khamis, The Riesz theorem in fuzzy
n-normed linear spaces, J. Appl. math & Informatics. 27 (2009) (2-4)
841 - 555.
[9] R. Malˇceski, Strong n-convex n-normed spaces, Mat. Bilten. 21 (47)
(1997) 81 - 102.
[10] A. Misiak, n-inner product spaces, Math. Nachr.140 (1989) 299 - 319.
[11] AL. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int.
J. Math. & Math. Sci. 24 (2005) 3963 - 3977.
[12] Papini, P. L., and Singer, I. Best coapproximation in normed linear
spaces, Monatshefte f¨ur Mathematik, 88 (1979) 27 - 44.
[13] G.S. Rao and R. Saravanan, Characterization of best uniform
coapproximation, Approximation Theory and its Applications. 15 (1999)
23 - 37.
[14] B. Surender Reddy, Some results on t-best approximation in fuzzy
anti-n-normed linear spaces, Int. J. Math. Archive. 2 (9) (2011) 1747
-1757.
[15] B. Surender Reddy, Fuzzy anti-n-normed linear space, J. Mathematics
and Technology. 2(1) February (2011) 14 - 26.
[16] S. M. Vaezpour and F. Karimi, t-Best approximation in fuzzy normed
spaces. Iranian J. Fuzzy Systems. 5 (2) (2008) 93 - 98.
[17] S. Vijayabalaji and N. Thillaigovindan, Complete fuzzy n-normed linear
space, Journal of Fund. Sci.3 007) 119 - 126.
[1] T. Bag and T. K. Samanta, A comparative study of fuzzy norms on a
linear space, Fuzzy Sets and Systems. 159 (2008) 670 -684.
[2] C. Franchetti and M. Furi, Some characteristic properties of real Hilbert
spaces, Rev. Roumaine Math. Pures Appl. 17 (1972) 1045 - 1048.
[3] S. G¨ahler, Lineare 2-normierte R¨aume, Math. Nachr. 28 (1964) 1-43.
[4] S. G¨ahler and Unter Suchyngen U¨ ber Veralla gemeinerte m-metrische
R¨aume I, Math. Nachr. 40 (1969) 165 - 189.
[5] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math & Math.
Sci. 27(10) (2001) 631 - 639.
[6] Iqbal H. Jebril and T. K. Samanta, Fuzzy anti-normed space, J.
Mathematics and Technology, February (2010) 66 -77.
[7] A. K. Katsaras, Fuzzy topological vector spaces, Fuzzy Sets and Systems,
12 (1984) 143 - 154.
[8] J. Kavikumar, Y. B. Jun and Azme Khamis, The Riesz theorem in fuzzy
n-normed linear spaces, J. Appl. math & Informatics. 27 (2009) (2-4)
841 - 555.
[9] R. Malˇceski, Strong n-convex n-normed spaces, Mat. Bilten. 21 (47)
(1997) 81 - 102.
[10] A. Misiak, n-inner product spaces, Math. Nachr.140 (1989) 299 - 319.
[11] AL. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int.
J. Math. & Math. Sci. 24 (2005) 3963 - 3977.
[12] Papini, P. L., and Singer, I. Best coapproximation in normed linear
spaces, Monatshefte f¨ur Mathematik, 88 (1979) 27 - 44.
[13] G.S. Rao and R. Saravanan, Characterization of best uniform
coapproximation, Approximation Theory and its Applications. 15 (1999)
23 - 37.
[14] B. Surender Reddy, Some results on t-best approximation in fuzzy
anti-n-normed linear spaces, Int. J. Math. Archive. 2 (9) (2011) 1747
-1757.
[15] B. Surender Reddy, Fuzzy anti-n-normed linear space, J. Mathematics
and Technology. 2(1) February (2011) 14 - 26.
[16] S. M. Vaezpour and F. Karimi, t-Best approximation in fuzzy normed
spaces. Iranian J. Fuzzy Systems. 5 (2) (2008) 93 - 98.
[17] S. Vijayabalaji and N. Thillaigovindan, Complete fuzzy n-normed linear
space, Journal of Fund. Sci.3 007) 119 - 126.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:66822", author = "J. Kavikumar and N. S. Manian and M. B. K. Moorthy", title = "Best Coapproximation in Fuzzy Anti-n-Normed Spaces", abstract = "The main purpose of this paper is to consider the new kind of approximation which is called as t-best coapproximation in fuzzy n-normed spaces. The set of all t-best coapproximation define the t-coproximinal, t-co-Chebyshev and F-best coapproximation and then prove several theorems pertaining to this sets.
", keywords = "Fuzzy-n-normed space, best coapproximation,
co-proximinal, co-Chebyshev, F-best coapproximation, orthogonality", volume = "8", number = "1", pages = "225-4", }
