  We give some Korovkin-type theorems on convergence and estimates of rates of
approximations of nets of functions, satisfying suitable axioms, whose
particular cases are filter/ideal convergence, almost convergence and
triangular A-statistical convergence, where A is a non-negative summability
method. Furthermore, we give some applications to Mellin-type convolution and
bivariate Kantorovich-type discrete operators.
