Geodesic
A connection between the summability methods of Cesaro and Lambert
Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 521-526 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that if a series is $(C,k)$ summable for some $k>-1$, then it is $(L,\alpha)$ summable to the same sum for any $\alpha<2$. 
@article{MZM_1969_5_5_a2,
     author = {I. I. Zhogin},
     title = {A~connection between the summability methods of {Cesaro} and {Lambert}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {521--526},
     year = {1969},
     volume = {5},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a2/}
}
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I. I. Zhogin. A connection between the summability methods of Cesaro and Lambert. Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 521-526. http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a2/