Alienation of Drygas' and Cauchy's functional equations
Abstract
Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation
f(x + y) + g(x + y) + g(x - y) = f(x)f(y) + 2g(x) + g(y) + g(-y).
We also consider an analogous problem for Drygas’ and the additive Cauchy functional equations as well as for Drygas’ and the logarithmic Cauchy functional equations. Interesting consequences of these results are presented.
Keywords
alienation; exponential Cauchy equation; additive Cauchy equation; logarithmic Cauchy equation; Drygas' functional equation
References
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Department of Mathematics E.N.S.A.M, Moulay ISMAIL University, Morocco Morocco
https://orcid.org/0000-0003-3708-3164
Department of Mathematics E.N.S.A.M, Moulay ISMAIL University, Morocco Morocco
Department of Mathematics, Faculty of Sciences, Chouaib Doukkali University, Morocco Morocco
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