1 Correction to: J Glob Optim https://doi.org/10.1007/s10898-021-01088-x

The results in this paper hold in the setting of a reflexive Banach space endowed with the weak topology, unless otherwise stated.

The assumption iv. in Theorem 2 becomes:

iv. whenever \(x,y \in C\), \(x_n\in C,\) \(x_n \rightharpoonup x\) and \(f(x_n, (1-t)x+ty) \ge 0\) for all \(t\in [0,1]\) and for all n, then \(f(x,y) \ge 0;\)

The proof of Proposition 2 becomes:


Let \(x,y \in C\), \(x_n\in C,\) \(x_n\rightharpoonup x\) and \(f(x_n, (1-t)x+ty) \ge 0\) for all \(t\in [0,1];\) in particular, \(f(x_n,x) \ge 0\) and \(f(x_n,y) \ge 0\). Then, \(\liminf _{n \rightarrow \infty } f(x_n,x) \ge 0\) and, by B-pseudomonotonicity, \(f(x,y) \ge \limsup _{n \rightarrow \infty } f(x_n,y) \ge 0\), for all \(y \in C\), that is \(f(x,y) \ge 0.\) \(\square \)

Finally, in Definition 1 convexity of the set C is not essential.