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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 373-375Stability of Cauchy-Jensen Mappings in...

Stability of Cauchy-Jensen Mappings in Non-Archimedean Normed Spaces

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Abstract:

In this paper, we prove stability of the CauchyJensen functional equation in non-Archimedean normed spaces, using the so-called direct method.

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Periodical:

Applied Mechanics and Materials (Volumes 373-375)

Pages:

1935-1938

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.373-375.1935

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Online since:

August 2013

Authors:

Hai Yan Xue, Pei Sheng Ji

Keywords:

Cauchy-Jensen Mapping, Non-Archimedean Space, Stability

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] S.M. Ulam, Some questions in analysis: 1, stability, Problems in Modern Mathematics, Science eds., Wiley, New York, 1964 (Chapter VI).

[2] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941) 222–224.

DOI: 10.1073/pnas.27.4.222

[3] Won-Gil Park, Jae-Hyeong Bae, On a Cauchy–Jensen functional equation and its stability, J. Math. Anal. Appl. 323 (2006) 634–643.

[4] V.A. Fa. ziev, T. Riedel, Stability of Jensen functional equation on semigroups, J. Math. Anal. Appl. 364 (2010) 341. 351.

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DOI: 10.1007/bf01831117

[6] D.H. Hyers, G. Isac, Th.M. Rassias, Stability of Functional Equations in Several Variables, Progr. Nonlinear Differential Equations Appl., vol. 34, Birkhäuser Boston, Inc., Boston, MA, (1998).

DOI: 10.1007/978-1-4612-1790-9