2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56788We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $τ$ strict contractions}, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems.in press in Publication RIMSMathematical PhysicsOperator Algebras47H10; 46N50text