Kernel function based interior-point methods for horizontal linear complementarity problems

Journal of Inequalities and Applications

Table 4 Conditions (a) and (b)

j	$t ψ_{j}^{''} (t) + ψ_{j}^{'} (t)$	$t ψ_{j}^{''} (t) - ψ_{j}^{'} (t)$
1	$2 e t + e^{p (g_{1} (t) - e)} g_{1} (t) t^{- 2 r - 1} (p r g_{1} (t) + r + r t^{r})$	$e^{p (g_{1} (t) - e)} g_{1} (t) t^{- 2 r - 1} (p r g_{1} (t) + r + (r + 2) t^{r})$
2	$2 t + e^{p (g_{2} (t) - 1)} g_{2} (t) t^{- 2 r - 1} (p r g_{2} (t) + r + r t^{r})$	$e^{p (g_{2} (t) - 1)} g_{2} (t) t^{- 2 r - 1} (p r g_{2} (t) + r + (r + 2) t^{r})$