Convergence theorem for finite family of lipschitzian demi-contractive semigroups
<p>Abstract</p> <p>Let <it>E </it>be a real Banach space and <it>K </it>be a nonempty, closed, and convex subset of <it>E</it>. Let <inline-formula><graphic file="1687-1812-2011-18-i1.gif"/></inline-formula> be a finit...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2011-01-01
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| Series: | Fixed Point Theory and Applications |
| Subjects: | |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/1/18 |
| Summary: | <p>Abstract</p> <p>Let <it>E </it>be a real Banach space and <it>K </it>be a nonempty, closed, and convex subset of <it>E</it>. Let <inline-formula><graphic file="1687-1812-2011-18-i1.gif"/></inline-formula> be a finite family of Lipschitzian demi-contractive semigroups of <it>K</it>, with sequences of bounded measurable functions <it>L<sub>i </sub></it>: [0, ∞) → (0, ∞) and bounded functions <it>λ<sub>i </sub></it>: [0, ∞) → (0, ∞), respectively, where <inline-formula><graphic file="1687-1812-2011-18-i2.gif"/></inline-formula>, <it>i </it>= 1,2, ..., <it>N</it>. Strong convergence theorem for common fixed point for finite family <inline-formula><graphic file="1687-1812-2011-18-i1.gif"/></inline-formula> is proved in a real Banch space. As an application, a new convergence theorem for finite family of Lipschitzian demi-contractive maps is also proved.</p> <p><b>Mathematics subject classification (2000) </b>47H09, 47J25</p> |
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| ISSN: | 1687-1820 1687-1812 |