The rate of weak convergence of convex type positive finite measure (Q921318)

The author obtains different exact estimates of \(\lambda\) for inequalities of the form \[ | \int_{M}f d\mu -f(x_ 0)| \leq | \mu (M)-1)| | f(x_ 0)| +\lambda \] wherein \(\mu\) is a positive measure on a nonempty convex subset M of a real normed space. This kind of inequality arises from quantitative Korovkin type theorems. The estimates improve earlier results of the author and others. Applications are also given in this paper.