On global approximation properties of abstract integral operators in Orlicz spaces and applications.
A modular convergence theorem for certain nonlinear integral operators with homogeneous kernel.
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
Approximation by nonlinear integral operators in some modular function spaces
Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function is estimated, where and K satisfies a generalized Lipschitz condition with respect to the second variable.
Nonlinear operators of integral type in some function spaces.
We give results about embeddings, approximation and convergence theorems for a class of general nonlinear operators of integral type in abstract modular function spaces. Thus we extend some previous result on the matter.
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...
Page 1