In this article, we consider the problem of pointwise convergence rates for density kernel estimator based on directional data.

In this paper,the pointwise convergence and divergence of a class of generalized Fourier series generated by piecewise linear spectral sequences are studied.

Effect of calculation parameters on convergence speed of one-dimensional transient heat transfer series solution;

Study on convergence speed of high order P type iterative learning control algorithm;

Analysis of convergence speed of repetitive control system;

Improvement of convergence rates for the empirical Bayes test problem in scale exponential family;

Mean convergence rate of derivatives approximation by Lagrange interpolation operators;

Making use of the formula of and the inequality of,this paper has deduced two types of probabilistic approximation of C-semigroups and the estimating of convergent rate.

It has been shown that the convergent rate .

Then,using Taylor expansion of the semigroup,Holder s inequality and estimations of moment-generating functions of some suitable random variables,some briefly probabilistic approximations and estimations of convergent rates are obtained for C-semigroups.