Rocky Mountain Journal of Mathematics

Cauchy-Rassias Stability of Sesquilinear $n$-Quadratic Mappings in Banach Modules

Chun-Gil Park and Sun-Young Jang
Source: Rocky Mountain J. Math. Volume 39, Number 6 (2009), 2015-2027.
First Page: Show Hide
Primary Subjects: 39B52, 47Jxx, 46L05
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1262271387
Digital Object Identifier: doi:10.1216/RMJ-2009-39-6-2015
Zentralblatt MATH identifier: 05652735
Mathematical Reviews number (MathSciNet): MR2575891

References

Y.J. Cho, P.C.S. Lin, S.S. Kim and A. Misiak, Theory of $2$-inner product spaces, Nova Science Publishers, New York, 2001.
Mathematical Reviews (MathSciNet): MR2017337
Zentralblatt MATH: 1016.46002
P.W. Cholewa, Remarks on the stability of functional equations, Aequat. Math. 27 (1984), 76-86.
Mathematical Reviews (MathSciNet): MR758860
Digital Object Identifier: doi:10.1007/BF02192660
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg 62 (1992), 59-64.
Mathematical Reviews (MathSciNet): MR1182841
R.V. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249-266.
Mathematical Reviews (MathSciNet): MR832356
Zentralblatt MATH: 0573.46034
A. Misiak, $n$-inner product spaces, Math. Nachr. 140 (1989), 299-319.
Mathematical Reviews (MathSciNet): MR1015402
Digital Object Identifier: doi:10.1002/mana.19891400121
--------, Orthogonality and orthogonormality in $n$-inner product spaces, Math. Nachr. 143 (1989), 249-261.
Mathematical Reviews (MathSciNet): MR1018246
Zentralblatt MATH: 0708.46025
Digital Object Identifier: doi:10.1002/mana.19891430119
C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl. 275 (2002), 711-720.
Mathematical Reviews (MathSciNet): MR1943774
Zentralblatt MATH: 1021.46037
Digital Object Identifier: doi:10.1016/S0022-247X(02)00386-4
--------, Generalized Hyers-Ulam-Rassias stability of $n$-sesquilinear-quadratic mappings on Banach modules over $C^*$-algebras, J. Comput. Appl. Math. 180 (2005), 279-291.
Mathematical Reviews (MathSciNet): MR2139833
Zentralblatt MATH: 1074.39031
Digital Object Identifier: doi:10.1016/j.cam.2004.11.001
--------, Multilinear Trif $d$-mappings in Banach modules over a $C^*$-algebra, Rocky Mountain J. Math. 35 (2005), 641-654.
Mathematical Reviews (MathSciNet): MR2135590
Digital Object Identifier: doi:10.1216/rmjm/1181069751
Project Euclid: euclid.rmjm/1181069751
Zentralblatt MATH: 1080.47036
J.M. Rassias and M.J. Rassia, On the Ulam stability of Jensen and Jensen type mappings on restricted domains, J. Math. Anal. Appl. 281 (2003), 516-524.
Mathematical Reviews (MathSciNet): MR1982670
Zentralblatt MATH: 1028.39011
Digital Object Identifier: doi:10.1016/S0022-247X(03)00136-7
Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
Mathematical Reviews (MathSciNet): MR507327
Zentralblatt MATH: 0398.47040
Digital Object Identifier: doi:10.2307/2042795
--------, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes-Bolyai 43 (1998), 89-124.
Mathematical Reviews (MathSciNet): MR1854544
--------, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), 352-378.
Mathematical Reviews (MathSciNet): MR1761936
Zentralblatt MATH: 0958.46022
Digital Object Identifier: doi:10.1006/jmaa.2000.6788
--------, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 264-284.
Mathematical Reviews (MathSciNet): MR1790409
Zentralblatt MATH: 0964.39026
Digital Object Identifier: doi:10.1006/jmaa.2000.7046
--------, On the stability of the quadratic functional equation, Mathematica, to appear.
Th.M. Rassias and P. Šemrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993), 325-338.
Mathematical Reviews (MathSciNet): MR1209322
Zentralblatt MATH: 0789.46037
Digital Object Identifier: doi:10.1006/jmaa.1993.1070
Th.M. Rassias and K. Shibata, Variational problem of some quadratic functionals in complex analysis, J. Math. Anal. Appl. 228 (1998), 234-253.
Mathematical Reviews (MathSciNet): MR1659917
Zentralblatt MATH: 0945.30023
Digital Object Identifier: doi:10.1006/jmaa.1998.6129
F. Skof, Proprietà locali e approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129.

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Rocky Mountain Journal of Mathematics

Rocky Mountain Journal of Mathematics