We only show the case (j=3); the remaining three cases can be verified similarly.
Proof We address the proof of Γ n P ( Y ), where the other cases can be verified in an analogous method.
Indeed, for any (xin[0,2)), we have that (Sx=0). Thus, vert Sx-0vert ^{2}=0leq vert x-0vert ^{2}. The other cases can be verified similarly. It is worth mentioning that S is neither nonexpansive nor continuous. Let (beta_{n,k}=0) and (alpha_{n}=frac{1}{4}) for all (n,kgeq1).
Afterwards, the HDL code can be verified.
For this case, it can be verified that the stability conditions in [10, 13] are not applicable when h d ≥ 1.
Therefore, for this specialized case, it can be verified theoretically that the proposed LTVFF-DRLS and LCTVFF-DRLS algorithms are convergent in terms of the learning curve and the convergence rate is related to the varying forgetting factors.
Under this condition, x 2 < y 2 and u 2 > v 2. Then by the condition y 2 ≤ v 2, we have x 2 < y 2 ≤ v 2 < u 2, which contradicts that x 2 ≥ u 2. In all the above cases, it can be verified that (4.1) is satisfied.
The first is verificationism, according to which a (declarative) sentence is meaningful just in case its truth value can be verified.
However, our proposed policy can still be beneficial even to practical cases where not all these assumptions can be verified.
The existence of the measure can be verified in limited cases, as will be discussed later.
The condition (ii) of the last lemma can be verified in some cases by means of the following lemma (cf. [[8], Lemma 10]).
