Abrishami-Moghaddam, M.; Sistani, T. Some results on best coapproximation in fuzzy normed spaces. (English) Zbl 1375.46059 Afr. Mat. 25, No. 3, 539-548 (2014). Summary: In this paper we study the concept of \(t\)-best coapproximation in fuzzy normed spaces. We introduce the notions of \(t\)-best coapproximation, \(t\)-coproximinal sets, \(t\)-coChebyshev sets and \(t\)-orthogonality and prove some interesting theorems to characterization of \(t\)-best coapproximation elements. Also we develop the theory of \(t\)-best coapproximation in quotient spaces. Cited in 1 Document MSC: 46S40 Fuzzy functional analysis 41A50 Best approximation, Chebyshev systems Keywords:fuzzy normed spaces; \(t\)-best coapproximation; \(t\)-coproximinal sets; \(t\)-coChebyshev sets; \(t\)-quasi coChebyshev sets; \(t\)-orthogonality PDFBibTeX XMLCite \textit{M. Abrishami-Moghaddam} and \textit{T. Sistani}, Afr. Mat. 25, No. 3, 539--548 (2014; Zbl 1375.46059) Full Text: DOI References: [1] Bag, T., Samanta, S.K.: Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math. 11(3), 678-705 (2003) · Zbl 1045.46048 [2] Cheng, S.C., Mordeson, J.N.: Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86, 429-436 (1994) · Zbl 0829.47063 [3] Franchetti, C., Furi, M.: Some characteristic properties of real Hilbert spaces. Rev. Roumaine Math. Pures Appl. 17, 1045-1048 (1972) · Zbl 0245.46024 [4] Mazaheri, H., Modarress, S.M.: Some results concerning proximinality and coproximinality. Nonlinear Anal. 62(6), 1123-1126 (2005) · Zbl 1075.41017 · doi:10.1016/j.na.2005.04.024 [5] Narang, T.D., Singh, S.P.: Best coapproximation in metric linear Spaces. Tamkang J. Math. 30(4), 243-254 (1999) [6] Papini, P.L., Singer, I.: Best coapproximation in normed linear spaces. Monatshefte für Mathematik 88, 27-44 (1979) · Zbl 0421.41017 · doi:10.1007/BF01305855 [7] Rao, G.S., Saravanan, R.: Characterization of best uniform coapproximation. Approx. Theory Appl. 15(1), 23-37 (1999) · Zbl 0938.41017 [8] Saadati, R., Vaezpour, S.M.: Some results on fuzzy Banach spaces. J. Appl. Math. Comput. 17(1-2), 475-484 (2005) · Zbl 1077.46060 · doi:10.1007/BF02936069 [9] Vaezpour, S.M., Karimi, F.: t-Best approximation in fuzzy normed spaces. Iranian J. Fuzzy Syst. 5(2), 93-99 (2008) · Zbl 1171.46051 [10] Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X 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.