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Then, corollary 1 follows.

Hence, Lemma 1 follows.

Estimate (1) follows.

Claim (1) follows readily from this observation.

(1) follows from [6], Corollary 16.

Therefore, part (1) follows easily from (2.2).

The continuity of (xlongmapsto M_{f,k} x,1)) follows.

(s^{star}in S_{1}) follows from Theorem 4.2.

The reduction of Ag+-1 follows a similar pattern as its redox reaction in more conventional electrochemical solvents.

The continuity of the operator (mathcal{W}_{1}) follows from that of f.

Since (tilde{delta}leqepsilon), the inequality (3.6) for the case (k=1) follows from (3.5).