Summary
Functional equations of the form
are investigated on ℝ and on more general domains. The paper is divided into five sections. After two introductory sections we solve in Section 3 two special cases of the equation
In Section 4 we prove that the solutions of (FE) under certain conditions are exponential polynomials. Finally, the general solutions of the equation
are determined in Section 5. The last equation contains as special cases the equations of d'Alembert, Cauchy, Lobachevskii, Jensen, Pexider, Wilson, the sine equation, etc.
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