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Stability of a Jensen's Functional Equation in Banach Spaces

Received: 15 July 2014     Accepted: 19 August 2014     Published: 20 September 2014
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Abstract

Our aim in this note is to study the Hyers -Ulam stability and we investigate the Hyers-Ulam stability of generalized Jensen's Functional Equation in Banach Spaces: f ((x + y)/2) = (f(x) + f(y))/2

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 4)
DOI 10.11648/j.pamj.20140304.13
Page(s) 92-94
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Hyers-Ulam Stability, Jensen's Functional Equation, Approximation Theory

References
[1] T. Aoki, on the stability of the linear transformation in banach spaces, j. Math. Soc.Japan, 2(1950)64-66.J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68–73.
[2] I D. H. Hyers."on the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A.27(1941),222-224.
[3] Z. Kominek, on a local stability of the jensen functional EQUATION, Demonstratio Math., 22 (1989),499-507.
[4] R TH.M. Rassiass, on the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72(1978),297-300.
[5] M. Ulam, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience, New York, NY, USA, 1960. 1 .
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  • APA Style

    Seyed Habib Shakoory. (2014). Stability of a Jensen's Functional Equation in Banach Spaces. Pure and Applied Mathematics Journal, 3(4), 92-94. https://doi.org/10.11648/j.pamj.20140304.13

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    ACS Style

    Seyed Habib Shakoory. Stability of a Jensen's Functional Equation in Banach Spaces. Pure Appl. Math. J. 2014, 3(4), 92-94. doi: 10.11648/j.pamj.20140304.13

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    AMA Style

    Seyed Habib Shakoory. Stability of a Jensen's Functional Equation in Banach Spaces. Pure Appl Math J. 2014;3(4):92-94. doi: 10.11648/j.pamj.20140304.13

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  • @article{10.11648/j.pamj.20140304.13,
      author = {Seyed Habib Shakoory},
      title = {Stability of a Jensen's Functional Equation in Banach Spaces},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {4},
      pages = {92-94},
      doi = {10.11648/j.pamj.20140304.13},
      url = {https://doi.org/10.11648/j.pamj.20140304.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140304.13},
      abstract = {Our aim in this note is to study the Hyers -Ulam stability and we investigate the Hyers-Ulam stability of generalized Jensen's Functional Equation in Banach Spaces: f ((x + y)/2) = (f(x) + f(y))/2},
     year = {2014}
    }
    

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Author Information
  • Electrical and Computer Engineering Department, Seraj Higher Education Institute, Tabriz, Iran

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