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Approximation results for nonlinear integral operators in modular spaces and applications. (English) Zbl 1019.41013
Author’s abstract: We obtain modular convergence theorems in modular spaces for nets of operators of the form $(T_wf)(s)= \int_HK_w \biggl( s-h_w(t), f\bigl(h_w(t) \bigr)\biggr) d\mu_H(t), \;w>0,s\in G,$ where $$G$$ and $$H$$ are topological groups and $$\{h_w\}_{w>0}$$ is a family of homeomorphisms $$h_w:H\to h_w(H) \subset G$$. Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.

##### MSC:
 41A35 Approximation by operators (in particular, by integral operators) 46A80 Modular spaces 47G10 Integral operators 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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