These are related to the successive approximations of fixed points (via orbits) which converge to the fixed points in the modular sense, which is weaker than the metric convergence.
Convergences in norm and in modular sense are equivalent in X ρ if ρ ∈ Δ 2. Lemma 2.3 [[28], Lemma 2.4].
We establish convergence in the modular sense of an iteration scheme associated with a pair of mappings on a nonlinear domain in modular function spaces.
The purpose of this paper is to prove that the set of all common fixed points for a continuous nonexpansive semigroup of nonlinear mappings acting in modular function spaces can be represented as an intersection of fixed point sets of two nonexpansive mappings, where nonexpansiveness is understood in the modular sense.
Recently, Khamsi and Kozlowski presented a series of fixed point results for pointwise contractions, asymptotic pointwise contractions, pointwise nonexpansive and asymptotic pointwise nonexpansive mappings acting in modular functions spaces [6, 7] (all these should be considered in the modular sense, not in the sense of the corresponding norms).
In this regard, however, by considering time dependent signals we propose that frequency selectivity mechanisms like the ones studied here, can give more sense to the modular approach.
It makes sense to have different capabilities for different users and situations — that's what modular computing is all about.
Real metabolic networks are more modular (in the network-modularity sense) than random networks, but still far from, say, a system engineered by humans [18].
You leave Our Love a little baffled as to how Snaith came to the conclusion that this was "mind-numbingly simple" music: if it's not complicated in the overconvergent Siegel modular symbols sense, one of the things that makes it so compelling is its ambiguity – the feeling that you're never quite sure where it stands.
Let us first start this section with the definition of nonexpansive mappings in the modular metric sense.
