In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

We present a method to decrease the storage and communication complexity of the context-tree weighting method. This method is based on combining the estimated probability of a node in the context tree and weighted probabilities of its children in one single variable. This variable is represented by its logarithm.