Common fixed points of one-parameter nonexpansive semigroups in strictly convex Banach spaces
One of our main results is the following convergence theorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E, and let {T(t):t∈ℝ+} be a strongly continuous semigroup of nonexpansive mappings on C. Fix u∈C and t1,t2∈ℝ+ with t1<t2. Define a seq...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA/2006/58684 |
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| Summary: | One of our main results is the following convergence
theorem for one-parameter nonexpansive semigroups: let C be a bounded closed convex subset of a Hilbert space E, and let {T(t):t∈ℝ+} be a strongly continuous semigroup of nonexpansive mappings on C. Fix u∈C and t1,t2∈ℝ+ with t1<t2. Define a sequence {xn} in C by xn=(1−αn)/(t2−t1)∫t1t2T(s)xnds+αnu for n∈ℕ, where {αn} is a sequence in (0,1) converging to 0. Then {xn} converges strongly to a common fixed point of {T(t):t∈ℝ+}. |
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| ISSN: | 1085-3375 1687-0409 |