Kato proves this by direct calculation rather than the more general strong convergence method in his book which we discuss below.
For more results of strong convergence, complete convergence and the applications, one can refer to Hu et al. [25], Rosalsky and Volodin [26], Wang et al. [27], Wu et al. [28], Yang et al. [29], Yang and Hu [30], Wang et al. [31] and so on.
More results on lacunary strong convergence can be seen from [4 11].
(2) In most cases, strong convergence is more desirable than weak convergence.
Another possibility, however unlikely, is that albumin1 was a more recent acquisition that underwent strong convergence at the protein level with this legume lineage.
More precisely, they proved the following strong convergence theorem.
To be more precise, they proved the following strong convergence theorem.
Further, Kamimura and Takahashi (SIAM J. Optim. 13:938-945, 2003) extended Solodov and Svaiter's result to more general Banach spaces and obtained strong convergence of a proximal-type algorithm in Banach spaces.
Recently, Zhou and Gao [13] studied a new projection algorithm for strict quasi-ϕ-pseudocontractions and obtained a strong convergence theorem; for more details, see [13] and the reference therein.
In a uniformly smooth and strictly convex Banach space, which also enjoys the Kadec-Klee property, the author obtained a strong convergence theorem; for more details, see [25] and the references therein.
