A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings
Let E be a real Banach space, and K a closed convex nonempty subset of E. Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings. A simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient conditions for this sequence to converge to a common fixed point of {Ti}i...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/615107 |
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| Summary: | Let E be a real Banach space, and K a closed convex nonempty subset of E.
Let T1,T2,…,Tm:K→K be m total asymptotically nonexpansive mappings. A
simple iterative sequence {xn}n≥1 is constructed in E and necessary and sufficient
conditions for this sequence to converge to a common fixed point of {Ti}i=1m are given. Furthermore, in the case that E is a uniformly convex real Banach space,
strong convergence of the sequence {xn}n=1∞ to a common fixed point of the family
{Ti}i=1m is proved. Our recursion formula is much simpler and much more applicable than those recently announced by several authors for the same problem. |
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| ISSN: | 0161-1712 1687-0425 |