On approximation properties of Urysohn integral operators
On approximation properties of Urysohn integral operators
Let \(G\) be a locally compact Hausdorff topological space provided with a Borel measure \(\mu\). There are studied problems of approximation of a function \(f\) by means of a family of operators \[ (T_wf)(s)= \int_GK_w \bigl (s,t,f(t)\bigr) d\mu(t),\quad w0\) (dependent on \(f)\) for functions \(f\) belonging to a modular space generated by the sum of modulars \(\rho+ \eta\) in \(L^0(G)\).
- University of Perugia Italy
Linear operator approximation theory, generalized Lipschitz condition, nonlinear integral operator, Modular approximation; generalized Lipschitz condition; singularity; non linear integral operators; regular families, Approximation by operators (in particular, by integral operators), modular approximation, Rate of convergence, degree of approximation, singularity
Linear operator approximation theory, generalized Lipschitz condition, nonlinear integral operator, Modular approximation; generalized Lipschitz condition; singularity; non linear integral operators; regular families, Approximation by operators (in particular, by integral operators), modular approximation, Rate of convergence, degree of approximation, singularity
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