Communications of the
Korean Mathematical Society CKMS

Assume $H_{i}:\Bbb R_{+} \times \Bbb R_{+} \rightarrow \Bbb R_{+}$ $(i=1,2)$ are monotonically increasing (in both variables), homogeneous mappings for which $H_{1}(tu,tv) = t^{p}H_{1}(u,v)$ $(p>0)$ and $H_{2}(tu,tv) = H_{2}(u,v)^{t^{q}}$ $(q\leq 1)$ hold for $t,u,v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto~[2], the superstability problems of the functional inequalities $\| f(x + y) - f(x)f(y) \| \leq H_{i}(\| x \|, \| y \|)$ shall be investigated.

Keywords: Functional equation, superstability

MSC numbers: Primary 39B72