... s−n1−1nn0Kum,vnumλ/rvnvn1−λ/sn1−1nn0Kum,vnumλ/rvnvn1−λ/sε/q.3.15The series is uniformly convergent for ε ≥ 0, so it haslimε → 0∞nn0Kum,vnumλ/rε/qvn1−λ/sε/qvn ωλm, s3.16 and for m>n0,thereexistsε0> ... {bn∞}∞nn0∈ qϕ and bq,ϕ> 0. Therefore, the inequality 3.36 keeps the form of the strictinequality when H →∞.Inviewof∞nn0ϕnbqn∞Tapp,ψ, inequality 3.27 holds and 3.27 ... International M athematical Forum,vol.2,no.37–40, pp. 1831–1837, 2007.5 W. Zhong, “A Hilbert-type linear operator with the norm and its applications,” Journal of Inequalities and Applications, vol....