Share This Article:

Orthogonal Stability of Mixed Additive-Quadratic Jensen Type Functional Equation in Multi-Banach Spaces

Full-Text HTML XML Download Download as PDF (Size:310KB) PP. 325-332
DOI: 10.4236/apm.2015.56031    2,073 Downloads   2,403 Views   Citations
Author(s)    Leave a comment

ABSTRACT

In this paper, we prove the Hyers-Ulam stability of the following mixed additive-quadratic Jensen type functional equation: 

Cite this paper

Yang, X. , Chang, L. and Liu, G. (2015) Orthogonal Stability of Mixed Additive-Quadratic Jensen Type Functional Equation in Multi-Banach Spaces. Advances in Pure Mathematics, 5, 325-332. doi: 10.4236/apm.2015.56031.

References

[1] Ulam, S.M. (1960) A Collection of the Mathematical Problems. Inderscience Publishers, New York.
[2] Hyers, D.H. (1941) On the Stability of the Linear Functional Equation. Proceedings of the National Academy of Sciences, 27, 222-224.
http://dx.doi.org/10.1073/pnas.27.4.222
[3] Rassias, Th.M. (1978) On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the American Mathematical Society, 72, 297-300.
http://dx.doi.org/10.1090/S0002-9939-1978-0507327-1
[4] Jung, S.M. (2011) Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis. Springer, New York.
http://dx.doi.org/10.1007/978-1-4419-9637-4
[5] Mihet, D. and Radu, V. (2008) On the Stability of the Additive Cauchy Functional Equation in Random Normed Spaces. Journal of Mathematical Analysis and Applications, 343, 567-572.
http://dx.doi.org/10.1016/j.jmaa.2008.01.100
[6] Zhao, X.P., Yang, X.Z. and Pang, C.T. (2013) Solution and Stability of a General Mixed Type Cubic and Quartic Functional Equation. Journal of Function Spaces and Applications, 2013, Article ID: 673810.
[7] Moslehian, M.S. and Rassias, Th.M. (2007) Orthogonal Stability of Additive Type Equations. Aequationes Mathematicae, 73, 249-259.
http://dx.doi.org/10.1007/s00010-006-2868-0
[8] Najati, A. (2008) On the Stability of a Quartic Functional Equation. Journal of Mathematical Analysis and Applications, 340, 569-574.
http://dx.doi.org/10.1016/j.jmaa.2007.08.048
[9] Park, C., Cho, Y. and Kenary, H.A. (2012) Orthogonal Stability of a Generalized Quadratic Functional Equation in Non-Archimedean Spaces. Journal of Mathematical Analysis and Applications, 14, 526-535.
[10] Yang, X., Chang, L., Liu, G. and Shen, G. (2015) Stability of Functional Equations in (n, β)-Normed Spaces. Journal of Inequalities and Applications, 2015, 112.
http://dx.doi.org/10.1186/s13660-015-0628-1
[11] Saadati, R. and Park, C. (2010) Non-Archimedean L-Fuzzy Normed Spaces and Stability of Functional Equations. Computers Mathematics with Applications, 60, 2488-2496.
http://dx.doi.org/10.1016/j.camwa.2010.08.055
[12] Pinsker, A.G. (1938) Sur une fonctionnelle dans l’espace de Hilbert. Comptes Rendus (Dokl.) de l’Académie des Sciences, URSS, 20, 411-414.
[13] Gudder, S. and Strawther, D. (1975) Orthogonally Additive and Orthogonally Increasing Functions on Vector Spaces. Pacific Journal of Mathematics, 58, 427-436.
http://dx.doi.org/10.2140/pjm.1975.58.427
[14] R?tz, J. (1985) On Orthogonally Additive Mappings. Aequationes Mathematicae, 28, 35-49.
http://dx.doi.org/10.1007/BF02189390
[15] R?tz, J. and Szabó, G. (1989) On Orthogonally Additive Mappings IV. Aequationes Mathematicae, 38, 73-85.
http://dx.doi.org/10.1007/BF01839496
[16] Kenary, H.A. and Cho, Y. (2011) Stability of Mixed Additive-Quadratic Jensen Type Functional Equation in Various Spaces. Computers Mathematics with Applications, 61, 2704-2724.
http://dx.doi.org/10.1016/j.camwa.2011.03.024
[17] Dales, H.G. and Moslehian, M.S. (Preprint) Multi-Normed Spaces and Multi-Banach Algebras.
[18] Dales, H.G. and Moslehian, M.S. (2007) Stability of Mappings on Multi-Normed Spaces. Glasgow Mathematical Journal, 49, 321-332.
http://dx.doi.org/10.1017/S0017089507003552
[19] Moslehian, M.S. (2008) Superstability of Higher Derivations in Multi-Banach Algebras. Tamsui Oxford Journal of Information and Mathematical Sciences, 24, 417-427.
[20] Moslehian, M.S., Nikodem, K. and Popa, D. (2009) Asymptotic Aspect of the Quadratic Functional Equation on Multi-
Normed Spaces. Journal of Mathematical Analysis and Applications, 355, 717-724.
http://dx.doi.org/10.1016/j.jmaa.2009.02.017
[21] Moslehian, M.S. and Srivastava, H.M. (2010) Jensen’s Functional Equation in Multi-Normed Spaces. Taiwanese Journal of Mathematics, 14, 453-462.
[22] Wang, L., Liu, B. and Bai, R. (2010) Stability of a Mixed Type Functional Equation on Multi-Banach Spaces: A Fixed Point Approach. Fixed Point Theory and Application, 2010, Article ID: 283827, 9 p.
[23] Diaz, J.B. and Margolis, B. (1968) A Fixed Point Theorem of the Alternative for Contractions on Generalized Complete Metric Space. Bulletin of the American Mathematical Society, 74, 305-309.
http://dx.doi.org/10.1090/S0002-9904-1968-11933-0

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.