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 ${\displaystyle f\in {(L⁰\left(G\right))}_{\varrho +\eta }\cap DomT}$ is estimated, where ${\displaystyle \left(Tf\right)\left(s\right)={\int }_{G}K(t-s,f\left(t\right))dt}$ and K satisfies a generalized Lipschitz condition with respect to the second variable.