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Quadratic Differences that Depend on the Product of Arguments

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Abstract

In this paper, we determine all functions ƒ, defined on a field K (belonging to a certain class) and taking values in an abelian group, such that the quadratic difference ƒ(x + y) + ƒ(x − y) − 2ƒ(x) − 2ƒ(y) depends only on the product xy for all x, y ∈ K. Using this result, we find the general solution of the functional equation ƒ1(x + y) + ƒ2(x − y) = ƒ3(x) + ƒ4(y) + g(xy).

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References

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Authors and Affiliations

  1. Department of Applied Mathematics, South China University of Technology, Guangzhou, People’s Republic of China

    J. K. Chung

  2. Department of Mathematics Marshall University, Huntington, West Virginia, 25755-2560, USA

    B. R. Ebanks

  3. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    C. T. Ng

  4. Department of Mathematics, University of Louisville, Louisville, Kentucky, 40292-0001, USA

    P. K. Sahoo & W. B. Zeng

Authors
  1. J. K. Chung
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  2. B. R. Ebanks
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  3. C. T. Ng
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  4. P. K. Sahoo
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  5. W. B. Zeng
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Chung, J.K., Ebanks, B.R., Ng, C.T. et al. Quadratic Differences that Depend on the Product of Arguments. Results. Math. 31, 53–74 (1997). https://doi.org/10.1007/BF03322151

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  • DOI: https://doi.org/10.1007/BF03322151

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