×

Schauder basis, separability, and approximation property in intuitionistic fuzzy normed space. (English) Zbl 1219.46070

Summary: We define and study the concepts of Schauder basis, separability, and approximation property in intuitionistic fuzzy normed spaces and establish some results related to these concepts. We also display here some interesting examples by using the classical sequence spaces \(\ell_p\) \((1\leq p\leq \infty)\).

MSC:

46S40 Fuzzy functional analysis
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] J. Schauder, “Zur Theorie stetiger Abbildungen in Funktionalräumen,” Mathematische Zeitschrift, vol. 26, no. 1, pp. 47-65, 1927. · doi:10.1007/BF01475440
[2] R. Saadati and J. H. Park, “On the intuitionistic fuzzy topological spaces,” Chaos, Solitons & Fractals, vol. 27, no. 2, pp. 331-344, 2006. · Zbl 1083.54514 · doi:10.1016/j.chaos.2005.03.019
[3] M. Mursaleen and S. A. Mohiuddine, “Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative,” Chaos, Solitons & Fractals, vol. 42, no. 2, pp. 1010-1015, 2009. · Zbl 1200.46068 · doi:10.1016/j.chaos.2009.02.041
[4] M. Mursaleen and S. A. Mohiuddine, “On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 142-149, 2009. · Zbl 1183.46070 · doi:10.1016/j.cam.2009.07.005
[5] M. Mursaleen, S. A. Mohiuddine, and O. H. H. Edely, “On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces,” Computers & Mathematics with Applications, vol. 59, no. 2, pp. 603-611, 2010. · Zbl 1189.40003 · doi:10.1016/j.camwa.2009.11.002
[6] A. Palomares, M. Pasadas, V. Ramírez, and M. Ruiz Galán, “Schauder bases in Banach spaces: application to numerical solutions of differential equations,” Computers & Mathematics with Applications, vol. 44, no. 5-6, pp. 619-622, 2002. · Zbl 1035.65082 · doi:10.1016/S0898-1221(02)00176-1
[7] Y. Yılmaz, “Schauder bases and approximation property in fuzzy normed spaces,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 1957-1964, 2010. · Zbl 1190.46058 · doi:10.1016/j.camwa.2009.11.014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.