Dirichlet summability and strong nonlinear ergodic theorems in Hilbert spaces
โ Scribed by Takeshi Yoshimoto
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 196 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
โฆ Synopsis
Let C be a non-empty closed convex subset of a real Hilbert space H. Following Goebel and Kirk, a mapping T : C โ C is called asymptotically non-expansive with Lipschitz constants { n} if T n x -T n y 6 (1 + n) x -y for all n ยฟ 0 and all x; y โ C, where n ยฟ 0 for all n ยฟ 0 and
๐ SIMILAR VOLUMES
In this paper, we first obtain a weak mean convergence theorem of Baillon's type for nonspreading mappings in a Hilbert space. Further, using an idea of mean convergence, we prove a strong convergence theorem for nonspreading mappings in a Hilbert space.
Weak and strong convergence theorems are proved in real Hilbert spaces for a new class of nonspreading-type mappings more general than the class studied recently in Kurokawa and Takahashi [Y. Kurokawa, W. Takahashi, Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces, No