Nonlinear Mean Ergodic Theorems for Semigroups in Hilbert Spaces
<p/> <p>Let <inline-formula><graphic file="1687-1812-2007-073246-i1.gif"/></inline-formula> be a nonempty subset (not necessarily closed and convex) of a Hilbert space and let <inline-formula><graphic file="1687-1812-2007-073246-i2.gif"/>...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2007/073246 |
| Summary: | <p/> <p>Let <inline-formula><graphic file="1687-1812-2007-073246-i1.gif"/></inline-formula> be a nonempty subset (not necessarily closed and convex) of a Hilbert space and let <inline-formula><graphic file="1687-1812-2007-073246-i2.gif"/></inline-formula> be a semigroup on <inline-formula><graphic file="1687-1812-2007-073246-i3.gif"/></inline-formula> and let <inline-formula><graphic file="1687-1812-2007-073246-i4.gif"/></inline-formula> be an almost orbit of <inline-formula><graphic file="1687-1812-2007-073246-i5.gif"/></inline-formula>. In this paper, we prove that every almost orbit of <inline-formula><graphic file="1687-1812-2007-073246-i6.gif"/></inline-formula> is almost weakly and strongly convergent to its asymptotic center.</p> |
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| ISSN: | 1687-1820 1687-1812 |