Erratum to: Semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem

1 Erratum to: Positivity DOI 10.1007/s11117-014-0273-9

The original publication of the article contains an error which need to be amended as mentioned below:

In the original paper, we obtained an important lemma (i.e. Lemma 3.1).

Lemma 3.1

For any given $f\in C^{*}\backslash \{0_{{Y^{*}}}\}.$ Suppose that the following conditions are satisfied:

• (i) $A(\cdot )$ is continuous with nonempty compact values on $\Lambda .$

• (ii) $F$ is u.s.c. with nonempty compact values on $B\times B\times \Lambda .$

• (iii) For any $\mu \in \Lambda ,$

  $$\begin{aligned} (inf_{{z \in F(x,y,\mu )}})f(z))(inf_{{z\in F(y,x,\mu )}}f(z))\le 0,\quad \forall x,y\in A(\mu ). \end{aligned}$$

• (iv) For any $\mu \in \Lambda ,$ assumption $(A)$ holds for $f.$

Then$,$ $S_{f}(\cdot )$ is l.s.c. on $\Lambda .$

In the proof of the lemma in the original paper, we need prove $y_{0}=x_{0}$ to obtain a contradiction. For the purpose, by applying (3) of the original paper and $inf_{{z\in F(x_{0},y_{0},\mu _{0})}}f(z)\le 0$, we obtained Page 6, line 14 of the original paper

$$\begin{aligned} inf_{{z \in F(y_{0},x_{0},\mu _{0})}}f(z)=0. \end{aligned}$$

(1)

Then, by assumption (iv), we got that $y_{0}=x_{0}$.

In fact, (1) should be replaced by $inf_{{z \in F(x_{0},y_{0},\mu _{0})}}f(z)=0$.