On consistency of summability methods generated by nonlinear integral operators (Q2733918)

Let \((G,\Sigma,\mu)\) be a measure space, where \(G\) is a nonempty set closed under the operation ``\(\cdot\)'', and let two filtered families of operators NEWLINE\[NEWLINE(T_{i,w} g)(t)= \int_G K^i_w(s, g(ts)) d\mu(s)\quad (w\in W,\;i= 1,2)NEWLINE\]NEWLINE be given. There are obtained sufficient conditions in order that the methods of summability defined by the families of operators \((T_{1,w})\) and \((T_{2,w})\) be consistent in a modular space \(L^0_\rho(G)\), generated by a modular \(\rho\) in the space \(L^0(G)\) of \(\Sigma\)-measurable and \(\mu\)-almost everywhere finite functions on \(G\).