TY - JOUR AU - Fadli, B. AU - Zeglami, D. AU - Kabbaj, S. PY - 2018/03/15 Y2 - 2024/03/29 TI - A variant of the quadratic functional equation on semigroups. JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 37 IS - 1 SE - DO - UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/2779 SP - 45-55 AB - <p>Let <em>S </em>be a semigroup, let <em>H</em> be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of <em>S</em>. We express the solutions <em>f</em> : <em>S</em> → <em>H</em> of the following variant of the quadratic functional equation</p><p><em>f</em>(<em>xy</em>) + <em>f</em>(σ(<em>y</em>)<em>x</em>) = 2<em>f</em>(<em>x</em>) + 2<em>f</em>(<em>y</em>), <em>x</em>, <em>y</em> ∈ <em>S</em>,</p><p>in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.</p> ER -