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COMMON FIXED POINTS FOR SEMIGROUPS OF POINTWISE LIPSCHITZIAN MAPPINGS IN BANACH SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 84 / Issue 3 / December 2011
- Published online by Cambridge University Press:
- 26 September 2011, pp. 353-361
- Print publication:
- December 2011
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- Article
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Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the existence of common fixed points for pointwise Lipschitzian semigroups of nonlinear mappings Tt:C→C, where each Tt is pointwise Lipschitzian. The latter means that there exists a family of functions αt:C→[0,∞) such that
for x,y∈C. We also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Fréchet derivatives.
for 