for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

For Fr$acute{mathbf{text{e}}}$chet algebras $(A, (p_n))$ and $(B, (q_n))$, a linear map $T:Arightarrow B$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(Tab - Ta Tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{N}$, $a, b in A$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$...