  In this paper we introduce the notion of $\Delta$-weak character amenable
Banach algebras and investigate $\Delta$-weak character amenability of certain
Banach algebras such as projective tensor product $A\widehat{\otimes}B$, Lau
product $A\times_TB$ for every Banach algebra $ A$ and $B$, where $T$ be a
homomorphism from $B$ into $A$, abstract Segal algebras and module extension
Banach algebras.
