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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 $(q_n)$,...

In this paper we introduce a new notion of weakly m-continuous functions as functions from a set satisfying some minimal conditions into a topological spaces. We obtain some characterizations and several properties of such functions. Moreover, we define strongly m-closed graphs, m-compactness and m-connectedness and investigate the relationship between their properties and weakly m-continuous f...

In this paper we discuss a new type of continuous functions called almost slightly νg−continuous functions; its properties and interrelation with other continuous functions are studied.