Hyers-Ulam Stability of Functional Equationf(3x) = 4f(3x − 3) + f(3x − 6)
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
Hyers-Ulam Stability of Functional Equationf(3x) = 4f(3x − 3) + f(3x − 6)

Authors: Soon-Mo Jung

Abstract:

The functional equation f(3x) = 4f(3x-3)+f(3x- 6) will be solved and its Hyers-Ulam stability will be also investigated in the class of functions f : R → X, where X is a real Banach space.

Keywords: Functional equation, Lucas sequence of the first kind, Hyers-Ulam stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334838

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1360

References:


[1] J. Baker, J. Lawrence and F. Zorzitto, The stability of the equation f(x+ y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), 242-246.
[2] J. Brzde┬©k, D. Popa and B. Xu, Hyers-Ulam stability for linear equations of higher orders, Acta Math. Hungar. 120 (2008), 1-8.
[3] S. Czerwik, Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press, Palm Harbor, 2003.
[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. Gˇavrutˇa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431- 436.
[7] R. Ger and P. ˇ Semrl, The stability of the exponential equation, Proc. Amer. Math. Soc. 124 (1996), 779-787.
[8] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222-224.
[9] D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkh¨auser, Boston, 1998.
[10] D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153.
[11] S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations, Dynamic Sys. Appl. 6 (1997), 541-566.
[12] S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001.
[13] S.-M. Jung, Hyers-Ulam stability of Fibonacci functional equation, Bull. Iranian Math. Soc., in press.
[14] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, New York, 2001.
[15] Z. Moszner, On the stability of functional equations, Aequationes Math. 77 (2009), 33-88.
[16] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
[17] Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23-130.
[18] Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284.
[19] L. Sz'ekelyhidi, On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc. 84 (1982), 95-96.
[20] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publ., New York, 1960.