Stability problem for Pexiderized Cauchy-Jensen type functional equations of fuzzy number-valued mappings

Document Type : Research Paper


Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran


We investigate the stability problems of the $n$-dimensional Cauchy-Jensen type and the n-dimensional Pexiderized Cauchy-Jensen type fuzzy number-valued functional equations in Banach spaces by using the metric defined on a fuzzy number space.
Under some suitable conditions, some properties of the solutions for these equations such as existence and uniqueness are discussed. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.