In the form of a T, a T-maze is an experimental design in which each trial consists of decisions between two or more options. It contains choices with particular kinds of symmetries that have gained considerable attention in psychology and learning theories. One of the simplest mazes utilized by rats is the T-maze since it requires just a single point of preference. At a T-maze base, the mouse chooses to turn right or left to get food. This paper aims at analyzing the rat’s behavior in such circumstances and proposing a suitable mathematical model for it. The existence and uniqueness of a solution to the proposed T-maze model are investigated by using the appropriate fixed point method.
In (Iida and Kasuga 2013), the authors described multiplicative (but not necessarily linear) isometries ofMp(X)ontoMp(X)in the case of positive integerp∈N, whereMp(X) (p≥1)is included in the Smirnov classN∗(X). In this paper, we will generalize the result to arbitrary (not necessarily positive integer) value of the exponents0<p<∞.
We characterize the boundedness and compactness of a Toeplitz-type operator on weighted Bergman spaces satisfying the Bekolle-Bonami condition in terms of the Berezin transform.
We present maximal and area integral characterizations of Bergman spaces in the unit ball ofℂn. The characterizations are in terms of maximal functions and area integral functions on Bergman balls involving the radial derivative, the complex gradient, and the invariant gradient. As an application, we obtain new maximal and area integral characterizations of Besov spaces. Moreover, we give an atomic decomposition of real-variable type with respect to Carleson tubes for Bergman spaces.
By using a suitable modification of the notion of a w-distance we obtain some fixed point results for generalized contractive set-valued maps on complete preordered quasi-metric spaces. We also show that several distinguished examples of non-metrizable quasi-metric spaces and of cones of asymmetric normed spaces admit w-distances of this type. Our results extend and generalize some well-known fixed point theorems.
