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Weak and strong convergence theorems for nonspreading-type mappings in Hilbert spaces

โœ Scribed by M.O. Osilike; F.O. Isiogugu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
225 KB
Volume
74
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

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, Nonlinear Anal. 73 (2010) 1562-1568]. We explored an auxiliary mapping in our theorems and proofs and this also yielded a strong convergence theorem of Halpern's type for our class of mappings and hence resolved in the affirmative an open problem posed by Kurokawa and Takahashi in their final remark for the case where the mapping T is averaged.

๐Ÿ“œ SIMILAR VOLUMES

Weak and strong convergence theorems for
Weak and strong convergence theorems for nonspreading mappings in Hilbert spaces
โœ Yu Kurokawa; Wataru Takahashi ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 259 KB

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.