Abstract

It is shown that every almost linear mapping <TEX>$h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$</TEX> of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,<TEX>$r\;{\neq}\;1$</TEX) holds for all <TEX>$x{\;}{\in}{\;}X$</TEX>, that every almost quadratic mapping <TEX>$h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$</TEX> of a complex normed space X to a complex normed space Y is a quadratic mapping when <TEX>$h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$</TEX> holds for all <TEX>$x{\;}{\in}{\;}X$</TEX>, and that every almost cubic mapping <TEX>$h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$</TEX> of a complex normed space X to a complex normed space Y is a cubic mapping when <TEX>$h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$</TEX> holds for all <TEX>$x{\;}{\in}{\;}X$</TEX>.