Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214220230201Stability and superstability of n-Jordan ∗-homomorphisms in Frechet locally C*-algebras2330655210.22075/ijnaa.2021.21584.2276ENKhatere GhasemiDepartment of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, IranShahram GhaffaryDepartment of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, IranJavad JamalzadehDepartment of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, Iran0000-0003-0031-1426Choonkil ParkResearch Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea0000-0001-6329-8228Journal Article20201015Using fixed point methods, we prove the Hyers-Ulam stability and the superstability of $n$-Jordan $*$-homomorphisms in Fr\'echet locally $C^*$-algebras for the generalized Jensen-type functional equation<br />$$r f\left(\frac{ a+b}{ r} \right) + r f\left( \frac{a-b}{r}\right) =2f(a),$$<br />where $r$ is a fixed real number greater than $1$.https://ijnaa.semnan.ac.ir/article_6552_5d89d79697658ee00c8ee6256f679439.pdf