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 $(q_n)$...

We prove a stability of weakly almost conformal mappings in W 1,p(Ω;Rn) for p not too far below the dimension n by studying the W 1,pquasiconvex hull of the set Cn of conformal matrices. The study is based on coercivity estimates from the nonlinear Hodge decompositions and reverse Hölder inequalities from the Ekeland variational principle.

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero identity and $M$ be a graded $R$-module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.