Section 4 contains more lemmas
than the ones needed to prove Theorem 1 and even so in many places we know how to improve the lemmas
Since [absolute value of ([f.sup.(n)])] is r-convex function, for r [not equal to] 0, the use of Lemma
The next result follows obviously from the proof of Lemmas
3 and 4.
2.3 ([2, Theorem 2.3, Corollary 3.7, Theorem 3.10]).
In this subsection, we state some technical lemmas
which are required in proof of the convergence analysis of the algorithm.
We need the following lemmas
for proof of our main result.
Then, by using Lemmas
3 and 8, we have the following.
In order to prove our conclusions, we need several lemmas
. The following [L.sup.p]-boundedness result for commutator [b, [T.sub.[OMEGA]]] on function spaces was proved in .
By the definition of Resistance-Harary index and by Lemma
1, we have
. In order to prove Theorem 1.4, we need some lemmas
[E.sub.3)](1; F') = [E.sub.3)](1; G'), by Lemmas
2.2,2.3,2.4 and 2.7 we get f [equivalent to] g.
10 and 5, there is a constant C with [mathematical expression not reproducible] for all n.