• Honam Mathematical Journal
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• v.27 no.4
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• pp.641-647
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• 2005

This note is a verification on the relations between multiplicative and almost multiplicative linear maps; and the continuity of almost multiplicative linear maps.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.199-207
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• 2009

This note is a verification on the relations between almost linear and nearly additive maps; and the continuity of almost multiplicative nearly additive maps. Also we consider the stability of nearly additive and almost linear maps.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.641-649
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• 2016

A linear functional T on a $Fr{\acute{e}}echet$ algebra (A, (pn)) is called almost multiplicative with respect to the sequence ($p_n$), if there exists ${\varepsilon}{\geq}0$ such that ${\mid}Tab-TaTb{\mid}{\leq}{\varepsilon}p_n(a)p_n(b)$ for all $n{\in}\mathbb{N}$ and for every $a,b{\in}A$. We show that an almost multiplicative linear functional on a $Fr{\acute{e}}echet$ algebra is either multiplicative or it is continuous, and hence every almost multiplicative linear functional on a functionally continuous $Fr{\acute{e}}echet$ algebra is continuous.