Some generalized quadratic functional equations on monoids
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We solve two Pexiderized extensions of the quadratic functional equation on monoids. The equation is extended by replacing the group inversion in the classical quadratic equation with an involution, which may be either homomorphic or anti-homomorphic. Also two extensions of the Drygas functional equation are solved in the same setting. In all results it is assumed that at least one unknown function is central.
KeywordsQuadratic functional equation Involution Drygas functional equation Semigroup Monoid Pexider equation
Mathematics Subject Classification39B52