Abstract:
W.A. Kirk and L.M. Saliga and then Y. Chen, Y.J. Cho and L. Yang introduced lower semicontinuity from
above, a generalization of sequential lower semicontinuity, and they showed that wellknown results, such
as Ekeland’s variational principle and Caristi’s fixed point theorem, remain still true under lower
semicontinuity from above. In a previous paper we introduced a new concept, that generalizes lower
semicontinuity from above. In the present one we continue such study, also introducing other two new
generalizations of lower semicontinuity from above; we study such extensions, compare each other five
concepts (sequential lower semicontinuity, lower semicontinuity from above, the one by us previously
introduced and the two here defined) and,in particular, we show that the above quoted wellknown results
remain still true under one of such our generalizations.
Keywords:
generalized sequential lower semicontinuity, sequential lower semicontinuity from above, convex function,
variational principles, fixed point theorems
MSC:
26, 54, 49
