The stability of fuzzy approximately Jordan mappings

  • N. Eghbali University of Mohaghegh Ardabili.
  • B. Farhadinia Quchan Institute of Engineering and Technology.
Palabras clave: Fuzzy normed space, Approximate Jordan map, Stability.


In this paper we introduce the concept of fuzzy approximately Jordan mappings in fuzzy algebras, and study some of their basic properties. The main purpose of this paper is to study the stability of fuzzy approximately Jordan mappings in fuzzy algebras.


[1] Z. Gajda, On stability of additive mappings, Intermat. J. Math. Sci., 14, pp. 431—434, (1991).

[2] P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184, pp. 431— 436, (1994).

[3] J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18, pp. 145—174, (1967).

[4] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci., U.S.A. 27, pp. 222—224, (1941).

[5] D. H. Hyers, G.Isac and Th. M. Rassias, Stability of functional equations in several variables, Birkh¨auser, Basel, (1998).

[6] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (2-3), pp. 125—153, (1992).

[7] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12, pp. 143—154, (1984).

[8] A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of HyersUlam-Rassias theorem, Fuzzy Sets and Systems, 159 (6), pp. 720—729, (2008).

[9] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, pp. 297—300, (1978).

[10] Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc., 173, pp. 325—338, (1993).

[11] S. M. Ulam, Problems in modern mathematics, Chap. VI, Science eds., wiley, New York, (1960).

[12] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8, pp. 338—353, (1965).
Cómo citar
Eghbali, N., & Farhadinia, B. (1). The stability of fuzzy approximately Jordan mappings. Proyecciones. Revista De Matemática, 32(2), 143-157.