Weak convergence theorems for nonexpansive mappings and semigroups in Banach spaces with Opial’s property
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- by T. Kuczumow PDF
- Proc. Amer. Math. Soc. 93 (1985), 430-432 Request permission
Abstract:
Let $X$ be a Banach space with Opial’s property, $C$ a weakly compact subset of $X$, $x \in C$ and $S$ a nonexpansive semigroup on $C$. Then ${\left \{ {S(t)x} \right \}_{t \geqslant 0}}$ converges weakly to a common fixed point of $S$ iff $S(t + h)x - S(t)x \rightharpoonup 0$ as $t \to \infty$ for all $h > 0$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 430-432
- MSC: Primary 47H20; Secondary 47H09
- DOI: https://doi.org/10.1090/S0002-9939-1985-0773996-8
- MathSciNet review: 773996