Generalizations of Sequential Lower Semicontinuity
In [7] W.A. Kirk and L.M. Saliga and in [3] Y. Chen, Y.J. Cho and L. Yang introduced lower semicontinuity from above, a generalization of sequential lower semicontinuity, and they showed that well-known results, such as some sufficient conditions for the existence of minima, Ekeland's variational principle and Caristi's fixed point theorem, remain still true under lower semicontinuity from above. In the second of the above papers the authors also conjectured that, for convex functions on normed...