How to test the uniform convergence of a function series, without Weierstrass M-test

A function series $$\sum f_n(x)$$ is pointwise convergent in $$A_p$$ if $$\forall x\in A_p$$, $$\sum f_n(x)$$ converges.

It is totally convergent in $$A_p$$ if it passes the Weierstrass M-test. If a series passes the M-test, then it is also uniformly and pointwise convergent.

I have problems when I have to determine the uniform convergence when a series is not totally convergent.

In practice, what methods can I use to test the uniform convergence without Weierstrass M-test?