TY - JOUR
TI - A Minimax Theorem for -Valued Functions on Random Normed Modules
VL - 2013
PY - 2013
DA - 2013/10/05
DO - 10.1155/2013/704251
UR - https://doi.org/10.1155/2013/704251
AB - We generalize the well-known minimax theorems to -valued functions on random normed modules. We first give some basic properties of an -valued lower semicontinuous function on a random normed module under the two kinds of topologies, namely, the ()-topology and the locally -convex topology. Then, we introduce the definition of random saddle points. Conditions for an -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 -valued functions in the framework of random normed modules and random conjugate spaces.
JF - Journal of Function Spaces and Applications
SN - 2314-8896
PB - Hindawi Publishing Corporation
SP - 704251
KW -
A2 - De Liu, Pei
AU - Zhao, Shien
AU - Zhao, Yuan
ER -