Communications of the
Korean Mathematical Society CKMS

Recently Ding [4, 5, 8] gives examples of his $FC$-spaces which are not $L$-spaces due to Ben-El-Mechaiekh et al. [1]. We show that they are actually $L$-spaces. We also clarify that all statements in [5] can be stated in corrected and generalized forms for the class of abstract convex spaces beyond $FC$-spaces.

Keywords: abstract convex space, KKM space, generalized ($G$-)convex space, $L$-space, minimax inequality, fixed point

MSC numbers: 47H04, 47H10, 49J27, 49J35, 54C60, 54H25, 91B50