Stability of kℓ-Cubic Functional Equation in Non-Archimedean L-Fuzzy Normed Spaces
Abstract
In this paper, we establish the generalized Hyers-Ulam stability result for the kℓ-cubic functional equation
(k-ℓ) f(kx+ℓy) + (k+ℓ) f(kx-ℓy) = 2k2ℓ2 f(x-y) + 2(k2-ℓ2) [k2 f(x) + ℓ2 f(y)]
where k and ℓ are non-zero integers with k ¹± ℓ, in the setting of non-Archimedean L-fuzzy normed spaces.
Keywords
Full Text:
PDFReferences
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 6466.
K.T. Atanassv, Intuituinistic fuzzy metric spaces, Fuzzy Sets and Systems, 20 (1986), 8796.
T. Bag and S.K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), 513547.
Z. Gajda, On stability of additive mappings, Intermat. J. Math. Sci., 14 (1991), 431434.
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431436.
J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145174.
O. Hadžić, E. Pap, M. Budincević, Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces, Kybernetica, 38 (2002), 363381.
D.H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (2-3) (1992), 125153.
D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA, 27 (1941), 222224.
K.W. Jun and H.M. Kim, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, J. Math. Anal. Appl., 274 (2002), 867878.
K.W. Jun, H.M. Kim and I.S. Chang, On the Hyers-Ulam-Rassias stability of an Euler-Lagrange type cubic functional equation, J. Comput. Anal. Appl., 7 (2005), 2133.
A.K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143154.
D. Mihet, Fuzzy-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems, 159 (2008), 739744.
A.K. Mirmostafaee and M.S. Moslehian, Fuzzy approximately cubic mappings, Inf. Sci., 178 (2008), 37913798.
A.K. Mirmostafaee and M.S. Moslehian, Stability of additive mappings in non-Archimedean fuzzy normed spaces, Fuzzy Sets and Systems, 160 (2009), 16431652.
M. Mursaleen and S.A. Mohiuddine, On stability of a cubic functional equation in intuitionistic fuzzy normed spaces, Choas, Solutions and Fractals, 42 (2009), 29973005.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297300.
B. Schweizer and A. Sklar, Probabilistic metric spaces, Elsevier, North Holand, New York, (1983).
S. Shekari, R. Saadati and C. Park, Stability of the quadratic functional equation in non-Archimedean L-fuzzy normed spaces, Int. J. Nonlinear Anal. Appl., 1 2 (2010), 7283.
R. Saadati and C. Park, Non-Archimedean L-fuzzy normed spaces and stability of functional equations, Computers and Mathematics with Applications, 60 (2010), 24882496.
S.M. Ulam, Problems in modern mathematics, Chap. VI, Science eds., wiley, New York, 1960.
L.A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338353.
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.