Some new results on approximation in fuzzy 2-normed spaces

In this paper, we define a fuzzy 2-normed space and study the concept of best approximation in fuzzy 2-normed spaces (FTNS). We also define a set of best approximations, proximal set and approximatively compact set and prove some interesting results in this new setup.

[1]  A. K. Katsaras,et al.  Fuzzy topological vector spaces II , 1981 .

[2]  M. A. Erceg,et al.  Metric spaces in fuzzy set theory , 1979 .

[3]  H. H. Schaefer,et al.  Topological Vector Spaces , 1967 .

[4]  Mohammad Mursaleen,et al.  STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES IN INTUITIONISTIC FUZZY NORMED SPACES , 2009 .

[5]  Mohammad Mursaleen,et al.  Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative , 2009 .

[6]  Jian-zhong Xiao,et al.  Fuzzy normed space of operators and its completeness , 2003, Fuzzy Sets Syst..

[7]  Robin Giles,et al.  A computer program for fuzzy reasoning , 1980 .

[8]  S. M. Vaezpour,et al.  Best approximation on probabilistic normed spaces , 2009 .

[9]  S. K. Samanta,et al.  FINITE DIMENSIONAL FUZZY NORMED LINEAR SPACES , 2003 .

[10]  Q. M. Danish Lohani,et al.  On generalized statistical convergence in intuitionistic fuzzy normed space , 2009 .

[11]  Yilmaz Yilmaz,et al.  On some basic properties of differentiation in intuitionistic fuzzy normed spaces , 2010, Math. Comput. Model..

[12]  R. Bassanezi,et al.  Fuzzy modelling in population dynamics , 2000 .

[13]  S. Gähler,et al.  2-metrische Räume und ihre topologische Struktur†‡‡ , 1963 .

[14]  S. A. Mohiuddine.  Stability of Jensen functional equation in intuitionistic fuzzy normed space , 2009 .

[15]  S. A. Mohiuddine,et al.  On stability of a cubic functional equation in intuitionistic fuzzy normed spaces , 2009 .

[16]  K. Zhao,et al.  Random hopping among localized states and charge fluctuation at disordered surfaces , 1996 .

[17]  Mohsen Alimohammady,et al.  Compactness in fuzzy minimal spaces , 2006 .

[18]  Osmo Kaleva,et al.  On fuzzy metric spaces , 1984 .

[19]  C. Felbin,et al.  Finite dimensional fuzzy normed linear space , 1992 .

[20]  Ling Hong,et al.  Bifurcations of fuzzy nonlinear dynamical systems , 2006 .