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On an exponential-cosine functional equation

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Abstract

The exponential cosine functional equationf(x + y) + (2f 2(y) − f(2y))f(x − y) = 2f(x)f(y) is studied in some detail whenf is a complex valued function defined on a Banach space. We supply conditions which ensure continuity off everywhere under the hypothesis thatf is continuous at a point. We also find solutions of the functional equation which are continuous at some point.

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References

  1. J. Aczél,Lectures on functional equations and their applications, Academic Press, New York, 1966.MR 34: 8020

    Google Scholar 

  2. J. A. Baker, A sine functional equation,Aequationes Math. 4 (1970), 55–62.MR 42: 715

    Google Scholar 

  3. A. B. Buche, On an exponential-cosine operator-valued functional equation,Aequationes Math. 13 (1975), 233–241.MR 53: 3789

    Google Scholar 

  4. A.-L. Cauchy,Course d'analyse de l'École Polytechnique, I (Analyse algébrique), Paris, 1821

  5. Oeuvres complètes d'A.-L. Cauchy, Sér. 2, vol. 3, Paris, 1897; 98–113 and 220.

  6. T. M. Flett, Continuous solutions of the functional equationf(x + y) + f(x − y) = = 2f(x)f(y), Amer. Math. Monthly 70 (1963), 392–397.MR 26: 6635

    Google Scholar 

  7. P. L. Kannappan, The functional equationf(xy) + f(xy −1) = 2f(x)f(y) for groups,Proc. Amer. Math. Soc. 19 (1968), 69–74.MR 36: 3006

    Google Scholar 

  8. P. L. Kannappan andJ. A. Baker, A functional equation on a vector space,Acta Math. Acad. Sci. Hungar. 22 (1971), 199–201.MR 45: 5615

    Google Scholar 

  9. S. Kurepa, On some functional equations in Banach spaces,Studia Math. 19 (1960), 149–158.MR 22: 9755

    Google Scholar 

  10. S. Kurepa, A cosine functional equation in Banach algebras,Acta Sci. Math. (Szeged)23 (1962), 255–267.MR 26: 2901

    Google Scholar 

  11. H. Singh andH. L. Vasudeva, Exponential-cosine operator-valued functional equation in the strong operator topology,Aequationes Math. 27 (1984), 187–197.MR 85k: 47085

    Google Scholar 

  12. M. Sova, Cosine operator functions,Rozprawy Math. 49 (1966), 47 pp.MR 33: 1745

  13. H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins,Math. Ann. 77 (1916), 313–352

    Google Scholar 

  14. H. Weyl,Gesammelte Abhandlungen, I, Springer, Berlin, 1968; 563–599

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Panjab University, 160014, Chandigarh, India

    J. C. Parnami & H. L. Vasudeva

  2. Department of Statistics, Panjab University, 160014, Chandigarh, India

    H. Singh

Authors
  1. J. C. Parnami
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  2. H. Singh
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  3. H. L. Vasudeva
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Parnami, J.C., Singh, H. & Vasudeva, H.L. On an exponential-cosine functional equation. Period Math Hung 19, 287–297 (1988). https://doi.org/10.1007/BF01848837

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  • DOI: https://doi.org/10.1007/BF01848837

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