The extension is made for the theorem of [2], by considering the classes S
pr and C
r, 1<p≤2, r∈{0,1,2,…} instead of S
p and C. Namely, it is shown that the class S
pr is a subclass of C
r∩BV, 1<p≤2,r∈{0,1, 2,…}, where BV is the class of null sequences of bounded variation, and C
r, r∈{0,1,2…} is the extension of the Garrett-Stanojevci class.