Our starting point is the Mosco-convergence result due to Hess ((He'89]) for integrable multivalued supermartingales whose values may be unbounded, but are majorized by a w-ball-compact-valued function. It is shown that the convergence takes place also in the slice topology. In the case when both the underlying space X and its dual X have the Radon-Nikodym property a weaker compactness assumpti...

Brain oscillations in the theta frequency band (3-8 Hz) have been shown to be critically involved in human episodic memory retrieval. In prior work, both positive and negative relationships between cortical theta power and retrieval success have been reported. This study examined the hypothesis that slow and fast cortical theta oscillations at the edges of the traditional theta frequency band a...

We study convergence group actions on continua, and give a criterion which ensures that every global cut point is a parabolic fixed point. We apply this result to the case of boundaries of relatively hyperbolic groups, and consider implications for connectedness properties of such spaces.

Theta waves in the amygdala are known to be synchronized with theta waves in the hippocampus. Synchronization between amygdala and hippocampal theta waves is considered important for neuronal communication between these regions during the memory-retrieval process. These theta waves are also observed during rapid eye movement (REM) sleep. However, few studies have examined the mechanisms and fun...

Experiments were carried out in urethane-anesthetized rats in order to evaluate the hypothesis that the red nucleus has functional connections with the hippocampal formation. Depth profiles of electrical stimulation in Experiment 1 confirmed that stimulation administered to the red nucleus elicited theta field activity in the hippocampal formation with a linear relationship between stimulus int...

Experiments were carried out in urethane-anesthetized rats to evaluate the hypothesis that the red nucleus has functional connections with the hippocampal formation. Depth profiles of electrical stimulation in experiment 1 confirmed that stimulation administered to the red nucleus elicited theta field activity in the hippocampal formation with a linear relationship between stimulus intensity an...

We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

In this article, we introduce the multi-$m$-Jensen mappings and characterize them as a single equation. Using a fixed point theorem, we study the generalized Hyers-Ulam stability for such mappings. As a consequence, we show that every multi-$m$-Jensen mappings (under some conditions) is hyperstable.