Geodesic
Continuity of the Optimal Value Function under some Hyperspace Topologies
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 397-406
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We characterize UC, boundedly UC and reflexive spaces in terms of continuity of the optimal value function of abstract minimization problems with respect to some hyperspace topologies defined on the classes of nonempty closed and closed convex sets. 
@article{JCA_2005_12_2_JCA_2005_12_2_a9,
     author = {A. K. Chakrabarty and P. Shunmugaraj},
     title = {Continuity of the {Optimal} {Value} {Function} under some {Hyperspace} {Topologies}},
     journal = {Journal of convex analysis},
     pages = {397--406},
     year = {2005},
     volume = {12},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a9/}
}
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A. K. Chakrabarty; P. Shunmugaraj. Continuity of the Optimal Value Function under some Hyperspace Topologies. Journal of convex analysis, Tome 12 (2005) no. 2, pp. 397-406. http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a9/