A quadratic functional equation stability in 2-Banach spaces
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DOI:
https://doi.org/10.26637/MJM0804/0122Abstract
In this article, we discuss the analysis in 2-Banach Spaces of the stability problem of the quadratic functional equation
$$
h(x+y)-h(x-y)=h(2 x+y)-4 h(x)-h(y) .
$$
Keywords:
Quadratic functional equation, Intuitionistic fuzzy normed spaces, Hyers-Ulam stabilityMathematics Subject Classification:
Mathematics- Pages: 2045-2049
- Date Published: 01-10-2020
- Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)
Aoki.T., On the stability of the linear transformation in Banach spaces, J.Math. Soc. Japan, 2(1950), 64-66.
Arunkumar.M., Jayanthi.S., Hema Latha.S., Stability of quadratic derivations of Arun-quadratic functional equation, International Journal Mathematical Sciences and Engineering Applications, 5(2011), 433-443.
Baktash.E., Cho.Y.J., Jalili.M., Saadati.R., Vaezpour.S.M., On the stability of cubic mappings and quadratic mappings in random nomed spaces, J.Inequal. Appl.. (2008), Article ID 902187.
Chang.I.S and Jung.Y.S., Stability for the functional equation of cubic type, J. Math. Ana. And Appl., 334(2007), $88-96$.
EshaghiGordji.M., Khodaei.H and Rassias. J.M., Fixed point methods for the stability of general quadratic functional equation, Fixed Point Theory, 12( 2011), 71 -82.
EshaghiGordji.M., Park.C., Savadkouhi.M.B., The stability of a quadratic type functional equation with the fixed point alternative, Fixed Point Theory, 11(2010), 265 $-272$.
Gavruta.P., A generalization of the Hyers - Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436.
G'ahler.S, 2-metrische R"aume and ihretopologischeStruktur, Math. Nachr., (26)(1963), 115 - 148.
G''ahler.S, Lineare 2 - normierteR'aume, Math. Nachr., (28)(1964), 1 - 43.
Hyers.D.H., On the stability of the linear functional equation, Proc. Natl. Acad. Sci., 27(1941), 222 - 224.
Jung.Y.S., The Ulam-Gavruta-Rassias stability of module left derivations, J. Math. Anal. Appl., doi: 10.1016/j.jmaa.2007.07.003, 1 -9.
Kannappan.Pl., Quadratic functional equation inner product spaces, Results Math., 27(3-4)(1995), 368-372.
Lee.Y.S and Chung.S.Y., Stability of quartic functional equations in the spaces of generalized functions, $A d v$. In Diff. Equ., (2009), Art.ID 838347, 16 pp.
Mihet.D., Saadati.R and Vaezur.S.M., The stability of the quartic functional equation in random normed space, Acta Applicandae Math., 110(2)(2009), 797 - 803.
Park. C., Generalized Hyers -Ulam -Rassiasstabiulity of quadratic functional equations: a Fixed Point approach, Fixed Point Theory Appl., 2008, Art. ID 493751 ( 2008).
Rassias.Th.M., On the stability of the linear mapping in Banach Spaces, Proc. Amer. Math. Soc., 72(1978), 297300.
Saadati. R., Vaezpour. S.M., Cho.Y.J., A note to paper "On the Stability of Cubic mappings and quadratic mappings in random normed spaces", J. Inequal. Appl., (2009), Article ID 214530.
Ulam.S.M., Problems in Modern Mathematics, Rend. Chap. VI. Wiley, New York, (1960).
White. A, 2 - Banach spaces, Doctorial Diss., St. Louis Univ. 1968.
White. A, 2 - Banach spaces, Math. Nachr., (42)(1969), $43-60$
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