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We consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods.
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Accordingly, we defined a model incorporating hard convergence of projections onto predefined, static patch areas (Model II).
A corollary of this convergence of projections is that retrograde transport "diverges" from any point across the cortical sheet, leading to diffuse labeling of somata.
In the above 4 proposed mechanisms of multimodal interplay, the number of neurons involved or contributing to territories of overlap or to convergence of projections in some areas appears fairly modest and therefore of functionally limited influence.
Small injections into global patch areas resulted in diffuse labeling of somata across the simulated cortical sheet, reflecting the widespread convergence of projections into these locations (Fig. 5 b ).
Although such a kind of multimodal integration in the temporal domain cannot be excluded (in case, the inputs reach the cerebral cortex at the exact same time), it is less likely to provide massive multimodal interplay than an actual spatial convergence of projections.
We also consider the convergence of the projection method under some suitable conditions.
Gabay [2] has shown that the convergence of a projection method can be proved for cocoercive operators.
We show that the convergence of both projection methods is controlled by the ability of the spectral framework to approximate correctly the steady Stokes problem.
It is well known that the convergence of a projection method requires the operator to be strongly monotone and Lipschitz continuous.
In order to obtain convergence of the projection method for equilibrium problems, Tran et al. [5] introduced an extragradient method for pseudomonotone equilibrium problems, which is computationally expensive because of the two projections defined onto the constrained set.
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