New results on value functions and applications to MaxSup and MaxInf problems

In this paper, in the setting of sequential spaces, we consider the value functions vS and vI defined by vS (x) = supy∈K(x) f (x, y) and vI (x) = infy∈K(x) f (x, y), and we introduce sufficient conditions on the value functions and on the data, weaker than upper semicontinuity, which guarantee the existence of maximum for such functions. Various examples illustrate the results and the connections with previous results.  2004 Elsevier Inc. All rights reserved.