Strong Convergence Theorems for Nonexpansive Semigroups and Variational Inequalities in Banach Spaces
Let 𝑋 be a uniformly convex Banach space and 𝒮={𝑇(𝑠)∶0≤𝑠<∞} be a nonexpansive semigroup such that ⋂𝐹(𝒮)=𝑠>0𝐹(𝑇(𝑠))≠∅. Consider the iterative method that generates the sequence {𝑥𝑛} by the algorithm 𝑥𝑛+1=𝛼𝑛𝑓(𝑥𝑛)+𝛽𝑛𝑥𝑛+(1−𝛼𝑛−𝛽𝑛)(1/𝑠𝑛)∫𝑠𝑛0𝑇(𝑠)𝑥𝑛𝑑𝑠,𝑛≥0, where {𝛼𝑛}, {𝛽𝑛}, and {𝑠𝑛} are three sequence...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/641479 |
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