We redefine the space and state the results of [1] in this light.

Let be a semigroup of positive regular matrices .

A bounded sequence is said to be -*almost convergent* to the value if and only if , as uniformly in , where
and which is -transform of a sequence (see Mursaleen [2]). The number is called the generalized limit of , and we write . We write

Using the idea of -almost convergence, we define the following.

An infinite matrix is said to be -*almost conservative* if for all , and we denote it by . An infinite matrix is said to be -*strongly conservative* if for all , and we denote it by .

Now, we restate Theorem 11 and Theorem 15 of [1] as follows, respectively.

Theorem 11. *Let be a -almost conservative matrix. Then, one has
**
where .*

*Proof. *It follows on the same lines as of Theorem 11 [1] by only replacing by .

Theorem 15. *Let be a normal positive regular matrix. Let be an infinite matrix. Then, one has the following.*(i)*If , then
* (ii)*If , then
* *where for all .*(iii)*If , then
* *where is the composition of the matrices and ; that is, .*

*Proof. *It follows on the same lines as Theorem 15 of [1] by only replacing by .

*Remark 1 (see [2]). *If consists of the iterates of the operator defined on by , where is an injection of the set of positive integers into itself having no finite orbits, then -invariant mean is reduced to the -mean and -almost convergence is reduced to -convergence. In this case, our results are reduced to the results of [3].