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A modular convergence theorem for certain nonlinear integral operators with homogeneous kernel

Here we give modular estimates for nonlinear integral operators of the form ( Tf )(s )= � G K(s, t, f(t))dt in Orlicz spaces. Namely we obtain an estimate for the error of approximation Tf − f and as a consequence we state the main result, i.e. (Twf − f) VW −→ 0 with w ∈W .