On global approximation properties of abstract integral operators in Orlicz spaces and applications.
Approximation results for nonlinear integral operators in modular spaces and applications
We obtain modular convergence theorems in modular spaces for nets of operators of the form , w > 0, s ∈ G, where G and H are topological groups and is a family of homeomorphisms Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.
On pointwise convergence of nets of Mellin-Kantorovich convolution operators
Here we study pointwise approximation and asymptotic formulae for a class of Mellin-Kantorovich type integral operators, both in linear and nonlinear form.
Korovkin theorem in modular spaces
In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.
Uniform modular integrability and convergence properties for a class of Urysohn integral operators in function spaces
Abstract Korovkin-type theorems in modular spaces and applications
We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the...
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