Automatic continuity of almost conjugate Jordan homomorphism on Fr$acute{text{e}}$chet $Q$-algebras

Abstract

In this paper, the notation of almost conjugate Jordan homomorphism between Fr$acute{mathbf{text{e}}}$chet algebras is introduced. It is proven that, under special hypotheses, every almost conjugate Jordan homomorphism on Fr$acute{mathbf{text{e}}}$chet algebras is an (weakly) almost homomorphism. Also, the automatic continuity of them is generalized.