TY - JOUR
A2 - De Liu, Pei
AU - Zhao, Shien
AU - Zhao, Yuan
PY - 2013
DA - 2013/10/05
TI - A Minimax Theorem for -Valued Functions on Random Normed Modules
SP - 704251
VL - 2013
AB - We generalize the well-known minimax theorems to L¯0-valued functions on random normed modules. We first give some basic properties of an L0-valued lower semicontinuous function on a random normed module under the two kinds of topologies, namely, the (ε,λ)-topology and the locally L0-convex topology. Then, we introduce the definition of random saddle points. Conditions for an L0-valued function to have a random saddle point are given. The most greatest difference between our results and the classical minimax theorems is that we have to overcome the difficulty resulted from the lack of the condition of compactness. Finally, we, using relations between the two kinds of topologies, establish the minimax theorem of L¯0-valued functions in the framework of random normed modules and random conjugate spaces.
SN - 2314-8896
UR - https://doi.org/10.1155/2013/704251
DO - 10.1155/2013/704251
JF - Journal of Function Spaces and Applications
PB - Hindawi Publishing Corporation
KW -
ER -