Hyers-ulam Stability of Fibonacci Functional Equation in Modular Functional Spaces
-
2976
Downloads
-
4054
Views
Authors
Maryam Naderi Parizi
- Department of Mathematics, Payame noor University, Tehran, Iran.
Madjid Eshaghi Gordji
- Department of Mathematics, Semnan University ,P.O.BOX35195-363, Semnan. Iran.
Abstract
In this paper, we prove the Hyers-Ulam stability of functional equation
\(f(x)=f(x-1)+f(x-2)\)
which called the Fibonacci functional equation in modular functional space.
Share and Cite
ISRP Style
Maryam Naderi Parizi, Madjid Eshaghi Gordji, Hyers-ulam Stability of Fibonacci Functional Equation in Modular Functional Spaces, Journal of Mathematics and Computer Science, 10 (2014), no. 1, 1-6
AMA Style
Parizi Maryam Naderi, Gordji Madjid Eshaghi, Hyers-ulam Stability of Fibonacci Functional Equation in Modular Functional Spaces. J Math Comput SCI-JM. (2014); 10(1):1-6
Chicago/Turabian Style
Parizi, Maryam Naderi, Gordji, Madjid Eshaghi. "Hyers-ulam Stability of Fibonacci Functional Equation in Modular Functional Spaces." Journal of Mathematics and Computer Science, 10, no. 1 (2014): 1-6
Keywords
- Hyers-Ulam stability
- Fibonacci functional equation
- modular functional space.
MSC
References
-
[1]
M. Bidkham, M. Hosseini, Hyers-Ulam stability of \(k\)-Fibonaccifunctional equation, Internat. J. Nonlinear Anal. Appl. , 2 (2011), 42--49.
-
[2]
M. Bidkham, M. Hosseini, C. Park, M. Eshaghi Gordji, Nearly \((k,s)\) --Fibonacci functional equations in beta--normed spaces, Aequationes Math., 83 (2012), 131--141.
-
[3]
M. Eshaghi Gordji, H. Khodaei, Stability of Functional Equations, LAP LAMBERT Academic Publishing, (2010)
-
[4]
G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. , 50 (1995), 143--190.
-
[5]
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14 (1991), 431--434.
-
[6]
P. Gavrota, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431--436.
-
[7]
P. Gavruta, L. Gavruta, A new method for the generalized Hyers-Ulam-Rassias stability, Int. J. Nonlinear Anal. Appl., 1 (2010), 11--18.
-
[8]
R. Ger, P. Semrl, The stability of the exponential equation, Proc. Amer. Math. Soc., 124 (1996), 779--787.
-
[9]
D. H. Hyers, On the stability of the linearfunctional equation, Proc. Natl. Acad. Sci. USA , 27 (1941), 221--224.
-
[10]
D. H. Hyers, G. Isac, Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston (1998)
-
[11]
D. H. Hyers, Th. M. Rassias, Approximate homomorphisms, Aequationes Math. , 44 (1992), 125--153.
-
[12]
S. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor (2001)
-
[13]
S. Jung, Hyers-Ulam stability of Fibonacci functional equation, Bull. Iranian Math. Soc., 35 (2009), 217--227.
-
[14]
S. Jung, Hyers--Ulam--Rassias stability of functional equations in nonlinear analysis, Springer Optimization and Its Applications, 48, Springer, New York (2011)
-
[15]
J. Musielak, W. Orlicz, On modular spaces, Studia Mathematica., 18 (1959), 49--65.
-
[16]
H. Nakano , Modular semi-ordered spaces, Tokyo Mathematical Book Series, Maruzen Co. Ltd,Tokyo, Japan (1950)
-
[17]
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297--300.
-
[18]
Th. M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992), 125--153.
-
[19]
S. M. Ulam, Problems in Modern Mathematics, Chapter VI, Science ed., Wiley, New York (1940)