Nonlinear integral operators and applications

By Carlo Bardaro, J. Musielak, Gianluca Vinti. 2003

207 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/80464e0e94c2892a98914659a4714d2af95e0335

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In Computational Theory and Mathematics

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Citations in the corpus

Abstract Korovkin-type theorems in modular spaces and applications (2013, background): “Let us recall the notion of modular space [9, 28].”
Approximation of discontinuous signals by sampling Kantorovich series (2015, background): “, [13, 9]) its Fourier expansion is given by: Ψχ (x) = ∑”
Approximation Results in Orlicz Spaces for Sequences of Kantorovich Max-Product Neural Network Operators (2018, background): “etween Sobolev spaces. The modular functional corresponding to ϕγ is: Iϕγ [f] := Zb a (e|f(x)|γ −1) dx, f ∈ M([a,b]). For further details concerning Orlicz spaces and some their extensions, see e.g., [43, 44, 9, 2, 3, 11, 12, 15, 13]. 4 3 Sigmoidal functions and basic assumptions A measurable functi”
Approximation Results for a General Class of Kantorovich Type Operators (2014, background): “1) arises as a natural modification of the generalized sampling series in order to reduce time jitter errors; concerning sampling type series, the reader can see the book [10] (Chapt.”
A Korovkin theorem in multivariate modular function spaces (2009, background): “An abstract approach to the theory of approximation was given in its definite form in [4].”
Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes (2014, background): “ated with Lp convergence and weak compactness. However it has also many applications in several branches of Mathematics, for example in reconstruction of signals, integral and discrete operators (see [8, 9, 10, 5, 6, 7, 33, 24]). The Vitali theorem has been investigated even in the context of vector”
Approximation properties in abstract modular spaces for a class of general sampling-type operators (2006, methodology): “which represents a nonlinear version of the generalized sampling operator [9].”
Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces (2014, background): “We define the class Lip∞(ν), 0 < ν ≤ 1, as Lip∞(ν) := {f ∈ C(R) : ‖f(·)− f(·+ t)‖∞ = O(‖t‖2), as ‖t‖2 → 0} , where for any two functions f , g : R → R, f(t) = O(g(t)) as ‖t‖2 → 0 means that there exist constants C, γ > 0 such that |f(t)| ≤ C |g(t)| for every t ∈ R, with ‖t‖2 ≤ γ ([7, 46]).”