Document Type: Research Paper

Author

Department of Mathematics,Marand Branch, Islamic azad university, Marand, Iran.

Abstract

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $C\left (X, Y \right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

Keywords

Main Subjects

[1] C. Alegre and S. Romaguera, The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited, Abstr. Appl. Anal., (2014), article ID 151472.

[2] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, Journal of Fuzzy Mathematics, 11 (2003), pp. 687-705.

[3] S.C. Cheng and J.N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429-436, .

[4] M. Goudarzi and V.M. Vaezpour, Best Simultaneous approximation in fuzzy normed spaces, Iranian J. of Fuzzy Syst., 7 (2010), pp. 87-96.

[5] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), pp. 336-344.

[6] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, (1970).

[7] B. Schweizer and A. Sklar, Statistical metric spaces, Pac. J. Math., 10 (1960), pp. 313-334.

[8] V.M. Vaezpour and F. Karimi, t-best approximation in fuzzy normed spaces, Iranian J. of Fuzzy Syst., 5 (2008), pp. 93-99.

[9] G.A. Watson, A Characterization of Best Simultaneous Approximations, J. of Approximation Theory, 75 (1993), pp. 175-182 .

[10] G.A. Watson, Characterization of subdifferential of some matrix norm, Linear Algebra Appl., 170 (1992), pp. 33-45.