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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On a quadratic-trigonometric functional equation and some applications
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by J. K. Chung, B. R. Ebanks, C. T. Ng and P. K. Sahoo PDF
Trans. Amer. Math. Soc. 347 (1995), 1131-1161 Request permission

Erratum: Trans. Amer. Math. Soc. 349 (1997), 4691-4691.

Abstract:

Our main goal is to determine the general solution of the functional equation \[ \begin {array}{*{20}{c}} {{f_1}(xy) + {f_2}(x{y^{ - 1}}) = {f_3}(x) + {f_4}(y) + {f_5}(x){f_6}(y),} \\ {{f_i}(txy) = {f_i}(tyx)\qquad (i = 1,2)} \\ \end {array} \] where ${f_i}$ are complex-valued functions defined on a group. This equation contains, among others, an equation of H. Swiatak whose general solution was not known until now and an equation studied by K.S. Lau in connection with a characterization of Rao’s quadratic entropies. Special cases of this equation also include the Pexider, quadratic, d’Alembert and Wilson equations.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 1131-1161
  • MSC: Primary 39B52; Secondary 39B22, 39B32
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1290715-0
  • MathSciNet review: 1290715