  In this paper, we establish quantitative estimates for nonlinear sampling
Kantorovich operators in terms of the modulus of continuity in the setting of
Orlicz spaces. This general frame allows us to directly deduce some
quantitative estimates of approximation in $L^{p}$-spaces, $1\leq p<\infty $,
and in other well-known instances of Orlicz spaces, such as the Zygmung and the
exponential spaces. Further, the qualitative order of approximation has been
obtained assuming $f$ in suitable Lipschitz classes. The above estimates
achieved in the general setting of Orlicz spaces, have been also improved in
the $L^p$-case, using a direct approach suitable to this context. At the end,
we consider the particular cases of the nonlinear sampling Kantorovich
operators constructed by using some special kernels.
